I'm going to be honest with you. There isn't a set place for that sort of thing here. In-fact, there was a thread that discussed adding a section for private role-plays, but the idea was dismissed.
Simply post your idea for the roleplay in the
On-topic forum, stating that you are looking for a single person to play with, and then wait for replies. You can ask them to pm you if you want. (It is an
extremely good idea to include in the title that you are looking for a private roleplay. Even stating that you're looking for a single person may be a good idea, though lengthy titles are (by themselves) a turnoff)
Getting to know the people, and how they roleplay is essential to this though. Lurking through a few of the plays going on in your preferred forum may help you to get to know a few of the more active players.
And if you already have someone you're interested in role-playing with, then simply give them a pm. If they don't like the idea, there's plenty of other players to choose from.
Honestly, there is no 'proper' way to go about this. Just use common sense and your best manners and you should do fine.