1) Although it's harder to buy yourself a diplomatic victory now, gold is still really useful, especially when a civ gives out the "gold is temporarily more effective" quest or "needs gold after getting bullied" quest. Get a ton of money.
2) Keep an eye on quests that a lot of civs want completed. If a bunch of civs want a natural wonder, start exploring. If they want a Great Artist, do what you can to get one. And so on.
3) Use your spies to rig elections, except for maybe one spy on defense (until you get Constabulary, Police Station, and National Intelligence Agency). And use coups as well. Keep spies in the city states that enemy civs keep screwing around with.
4) Don't play against Austria.
5) If you're worried about losing city states to a certain civ and you're close to the vote, pull the good old "bribe everyone and then declare war" trick.
That's pretty much it. I see the extra votes from other civs as a bonus, but they aren't really necessary. Everyone always seems to get pissed off at me by the end of the game anyway.