Alright, then. I have the following years that I feel comfortable with:

1812. Empires are crumbling, Brits are being taken down a peg, Japan begins to emerge, the Ottomans are still kicking arse in the Balkans, a lot of Imperialism to still be done.

1836. Possible, and I just spent about an hour researching, so I feel a bot more comfortable. Duck would get to play Texas and stay independent.

1900. Nice and juicy turn-of-the-century. Cultural movements, even number, and new tech.

1910. Very close to WWI, right after I believe the Russian-Japanese War. I would give us four years to get ready for the war, and then we get a nice juicy centerpiece conflict to keep everybody on their toes.

1920. After the war, perhaps things go a different route. Perhaps the allies end up forgiving Germany's debt, perhaps Hitler never rises. Who knows?