you must have a city close to the other city with significant culture (1000+ should do) several of these if possible. Just produce library, temple and univeristy and you should be producing enough culture ot get one. note that if they are close to their capital it will be hard to get a flip, but if they are close to yours it will be easy. Also the larger the city is (popultation) the harder the flip will be. A garrison can weaken the chances of a flip, but it takes quite a bit to negate all effects. Also try to take some of their borders, because the more of their rightful ones they own (the 21 square surrounding it) the less likely the flip is, and foreign borders there help alot. If they have any people of yours int heir it will also be a lot easier. Hope htis helps.
