When you start a new game, you have the option to turn off city flipping from culture. This is how I've done my warmonger campaigns. In this case, you have to deal with a lot revolts (and the city will stop growing/producing for a few turns) but it beats having to retake it, or to declare war on another civ.
Universal Suffrage definitely helps though, by the time you have it, it should be easy to afford to rush Theatre, University, etc quickly. IMHO, slavery is not as useful in this case, as often times your pop is too small to even whip after conquest.
A final option (and this really works!) is the Culture Bomb aka Great Artist -- get a city specialized to make great people with an emphasis on artists. This takes a bit of planning as it takes a while to get Great People, but one well placed culture bomb can really make a difference.