Civ 5 Diplomatic Victory possible with defeated civs?

If the one remaining civ has 3 city-states that they have conquered, you can liberate them to get your 3 votes. Otherwise you can't get a Diplomatic victory after you undiplomatically crushed all those city-states. =)

City States can never be razed, and get a vote in the diplomatic election.

If you're trying for diplomacy, you may as well start some wars to liberate any conquered city-states (which will immediately push them to "allied" with you, garnering you their vote).

If you've been the one conquering city states, you might be out of luck.

Well... open up the trading screen and give the other major civ your city states. (S)He might choose to liberate them and then it's only a matter of supplanting her/him as it's ally. If (s)he just annexes it then simply re-capture it and try again.

Please note that this is a theory, I have not tried actually doing it in-game.

In the Brave New World expansion, diplomatic victory comes from getting lots of votes when the United Nations (what the World Congress becomes after most civilizations have hit the Atomic Age) holds an Elect World Leader vote.

Every time the vote fails to elect a leader, the two civilizations with the most votes get two more votes in all future World Congresses. This guarantees that, sooner or later, somebody will eventually get enough votes to win.