There are some things you can try. My favorite one is to immediately build workers until the city is down to size 1, while being careful not to allow it to grow in the meantime. I get free slave workers (no upkeep) while reducing the probability of a culture filp since I reduce the foreign citizen number. Then, I either keep the city if it suits my purposes or let it grow at size 3 and abandon it in order to avoid making other civs angry. (razing a city or abandoning a city with foreign population 50% or more causes a reputation hit).Actually if the AI has at least twice the amount of culture as you then you're better oft just razing them. For example in my last (Emperor-level) game was fighting Greece and tried to keep a town and Athens. Lost about 5 or 6 units in the town and Athens flipped as well. We both had Knights so couldn't leave either one empty. Had I simply razed them could've probably finished Greece off in one war. As it was it took two.
A captured city does not flip during the first turn, so you should load it with a lot of troops in order to kill the resistance (probably healing at the same time). Afterwards, you can either keep a lot of troops inside (civassist helps you figure out when the chance of flipping gets to zero) or keep no troops inside and be ready to reconquer the city.
You may also intentionaly starve the city fast, although I prefer getting workers.
Conquering the next city (there are some conditions about that) helps reducing the flip risk as well. In general, keeping the war going is a good idea as far as flips go.