Updated from least to most recent:
Headcanon: In the third grade, Maria wasn't going to get any Valentines in school so Coulson went back in time and gave her a ton to make her fell special cause he didn't want to see her cry and make her give up on love, even if they were from a secret admirer.
Headcanon within that headcanon: He dropped back to see her going to the dance with some dorky kid because she thought he had sent her the nice letters. Coulson was a little jealous but ended up making sure she had a fun night and that the dorky kid didn't do anything rude or stupid, as kids do.
Headcanon: (canon verse) Meeting Rose in the shop wasn't the first time he had met her, even before New Years Eve, he had gone back in time after they had fought after Father's Day. So in order to ensure that she somehow didn't end up never meeting him, he went further back in time and made sure she was hired to work in the shops so that one day, they would meet and he could save her. determined to protect her always.
Headcanon for C&C: (our verse) Coulson had debated telling Maria sooner but something always came up, be it a call from the TARDIS or from work and he chalked it up to the universe telling him that it wasn't meant to be, which really saddened him because he thought she'd make a great companion for his real life's adventures.
Headcanon: Whenever she thinks the Doctor isn't looking, she tries to do some reading up on Science and Junk because she's determined to make herself a better companion for him. She wants to know a little about what he rambles on about. One day she tries to surprise him with a comment about quantum physics and it turns out it was outdated information in the year 4029 which embarrasses Rose and she swats his arm for not taking her seriously and he apologizes because he finds her too cute and he tells her she shouldn't need to waste time reading when he could just read it to her before bed. They develop a new tradition where he reads her boring things and she falls asleep in his arms. Her plan was a total success.
Headcanon within your above headcanon: Coulson started the rumors himself because he knew he was a stud but wanted Maria to think that maybe someone else thought he was, thus giving her subliminal messages about him and her and how great they would be together. It hurts when she tries to correct the aliens when they travel but when she gives up, he feels like he's gotten a personal victory and he ends up taking Maria out to dinner...just cause. He puts the reservation under Mr and Mrs. Hotpants McStudmuffin and they laugh so hard, they can't enter the restaurant.
Headcanon within your headcanon: Rose was always really annoyed at the Doctor. It seemed whenever her birthday neared, he would swing over to some planet and they'd land themselves in trouble again. All she wanted was a normal birthday but she knew the Doctor wasn't normal. He gave her odd things from odd planets, sometimes saying her present was at the bottom of some volcano. She is tempted to push him in but is more happy to be running with him, than stuck at some lame party back home.
Headcanon: Coulson doesn't like Maria calling him Coulson when they're in the TARDIS because it's not who he is. But after some contemplation, he realizes he doesn't know who he is anymore and for the longest time he would sit around brooding. He would then realize that he was both the Doctor and Coulson because both parts of him got to spend time with an amazing woman and he didn't care what she called him, just as long as she did.
Headcanon: When she fell into Jack's arms, her heart fluttered a little. It wasn't the same though. Not like when she was with the Doctor. But there she was, in his arm, having a drink and dancin' a little and she didn't feel a thing, just a need to find her grumpy Doctor with the big ears. When she saw him again, she wanted to hug him but refrained because they had mattered to attend to. Rose was glad to be alone with the Doctor again, determined to pull him away from that wall so she could have him all to herself. But then he got distracted and she got a little upset. It wasn't until they got close and started to dance, that words and actions became meaningless as they just had each other where they belonged.
Headcanon: Coulson loves his shades, they make him look cool. Or so he says. Many have tried to prank him or steal them as a joke but they always on him at all times. He loves them. He wouldn't lend them to someone if they were forced to stare in the sunlight. Nope. They're his. He even had a name for them but he wouldn't tell anyone that. Once day when he see Maria crying at the office about some bad breakup, he decides to lend her his sunglasses so no one can see she was crying. He never got them back until a month later. They were set on his desk, polished and cleaned with a simple 'thank you' note attached. He had felt so naked without them for so long and never knew why she held onto them for an entire month.
Headcanon (our RP): From the moment she walked into class the day they got a new sub, her world had shifted somehow. She could feel something was just...different. She caught one look at the snazzy teacher and found herself even more perplexed. She took her seat and listened to ever dull word, her mind somehow wandered to her flyin' off, his voice like a lullaby. When class ended and people talked about the cute new teacher, something inside of her stirred and she knew she had to get to the bottom of this sensation, this new desire.
Headcanon: He's lived almost 1000 years yet he doesn't feel old. He may look old in human years but he doesn't feel old. He tells himself he's not. He knows when he does get past the 1000 mark, he will be very old and very tired. He considered checking in on his old companions but couldn't bring himself to make them suffer a dull 1000 birthday. He figure he'll stop by Maria's and see what she's up to, hoping that his timing will be slightly better than the last time he dropped in on her unexpectedly.
Headcanon: He once told her about regeneration and she didn't think much of it because he said it didn't happen a lot. But the more they spent time together and bonded over chips and tea, she began to worry that he could regenerate from the slightest of things. So she ended up becoming overbearing and it bothered him. They ended up fighting about who was looking after who and she stormed off. He ran after her and said that even if he did change, his heart wouldn't. She looked at him, then smacked him for being a totally cheesy idiot and they laughed it off.
Headcanon within a headcanon: He really hated hates. Some of his past rengerations like them, but why, he'd never know. Coulson did his best to avoid them when he walked around New York City. He liked dogs, they were man's best friend. When he once saw the cat people who serves as nurses, he couldn't help but cry out a little and run back to the TARDIS. He had no idea why he hated cats but he did. He didn't enjoy Maria's at all and tried to get her come over his place whenever they wanted to be alone. Of course she wouldn't budge so he had to endure a lot of crap from a fatass cat if he wanted to have some nice alone with with Maria. Sometimes he just wished he went home and took a shower, his suits were never the same.
Headcanon: After the event where the Dalek almost killed her, and him, she started to have nightmares. She would toss and turn and finally give up on getting any sleep. On the third night of no sleep she finally decided to find the Doctor's room. It took her the whole night in which she ended up getting even more scared and wound up crying in a hallway. The Doctor found her and went with her back to her room and sat with her while she slept in his arms. He stroked her hair and told her fairytales from distant planets until she fell into a deep sleep.
Headcanon: He once tried to tell Maria about who he really was. He did it over coffee when they were outside near Central Park. The two of them were joking around, talking about time travel and what ifs. He said he could travel through time AND space to which she laughed. His grin faltered slightly and he dropped the topic, not too keen on mentioning it again as it seemed just to be a source of hilarity to her, rather than wonder. Coulson never knew that she was actually interested but she laughed at something behind them.
Headcanon: Her mother died. Her mother died while she was away with the Doctor doing some crazy thing, this or that. Her mother died and she never got to say goodbye. She had asked too but the Doctor said she couldn't go back into the timeline. Rose stepped in front of her mother's grave and gave her own late goodbye and the Doctor came up behind her and reached for her hand. She folded her arms and simply headed off to the pub where she knew Mickey would be waiting with a pint.
Headcanon: Maria's bad habits were likely to get her killed one day, hell, so was his. The two had stepped out of the TARDIS and made their way into a cold planet, void of any life energy. They walked around for what felt like hours. As Coulson was scanning the area, that's when the ground opened up and swallowed them whole. They fought and fought but knew the end was coming. They said their goodbye and in his final bout of strength, he handed her the sonic screwdriver and yelled for her to push it. It sent her right back to the TARDIS, while he was swallowed whole.
Headcanon: It was hard to think when they were always running and running. It was even more hard to remember the Doctor prided himself on well, being a doctor. So after a bit of a nasty tumble during while on the planet Cheem, the Doctor scooped up his companion and brought her back to the infirmary of the TARDIS and patched up her banged up knee. Rose was a bit caught off guard by his tenderness as he was doting on her like an overprotective father. She thought it was cute though and it took three days before she managed to wave him away, insisting she was fine again.
Headcanon: They spent hours looking for the sunglasses, they checked all the planets they had just visited. But they were nowhere to be found! This sent Coulson into a spiral of manic depression which just amused Maria to no end. At one point they didn't travel at all and just stayed on Earth doing work. While the Doctor refused to fly without his favorite accessory, Maria decided to fly the TARDIS herself and find the damn things, she ended up getting stuck on the Moon and it was the first time she got Coulson to laugh ever since he misplaced his shades. He found them a week later in the refrigerator of the TARDIS. How did they even get there?
Headcanon: Maria and Rose grew up in the same apartment complex together, Maria taking Rose under her wing as an older sister figure may do. Rose always wanted siblings but her mother was against anymore mouths to feed. When Maria suddenly vanished one day, Rose grew worried, not knowing a man in a blue blox had carried her off into space. A few weeks passed and another blue box came down and invited Rose to come along. Both friends ended up getting whisked away by two different Doctors. They reunited when they were both taken hostage by the annoying Daleks. Needless to say, they had a lot more to gossip about.
Headcanon: Coulson could always get his favorite cup of coffee on a far away planet but sometimes he couldn't get to it because he had meeting so instead his second favorite would have to do. Maria made a pot of coffee every morning and everyone loved it so he always parked his TARDIS just on time to make it to when she was done making it for the other agents. He'd pour himself some and would hope to someday show her his favorite place, light years away. It wasn't until she leaned in and said she put a little exta love in his cup, that hers became his favorite of all.
Headcanon: The Doctor stumbled upon a large bang in the kitchen area of the TARDIS. He rushed to find Rose covered in half baked cake, flour and frosting. She said she tried to make him a cake for saving her from the stupid Cybermen again. They spent an hour cleaning up the mess all while Rose felt like an idiot. After she showed, she found the Doctor in her room, holding out a cup of tea for the poor girl. He brought up the fiasco a few times after that and Rose was determined to make a successful cake someday.