Also, they are programmed not to trade cities for other goods in any situation. Therefore, you cannot offer anything from your side in the deal.
You can ask them anything in peace negotiations. In peace nagotioations, you can offer gpt even with the worst reputation possible (this is very abusable to aquire techs) but when you want cities, you cannot give anything in the deal from your side. (Except for peace of course)
Primarily, they will give you more cities if you beat them more.
Also will they give more cities when you have units ready to take cities in one move. Losing things to the AI makes them less inclined to pay you cities. (or anthing else for that matter)
However, it seems to me that what they are willing to pay is a % of their total empire. Sometimes conquering more will make them pay less. I am not sure if this is true, it might also be that i have lost units in the attack or because i am now not threathening other cities anymore.
Cities that have a resource in their radius are worth much more to the AI and thus much harder to get from them.