I have found a very sucessfull way of stoping the Computer form expanding into your territory. What you do is pick a civ that get a special unit early on in the game. Then post units along the computer boarder so that when he sends out a settler with a spearman. Then wait for the settler to build a city. once the city is built attack and you can easly get the city.
Doing this will limit the computer form expanding into your territory and you can get a lot of free cities this way. Also attack some of there cities that are already big and have good defensive units. Just take a couple of cities at a time, then sue for peace. This way you chip away at the computer empire slowly. I was able to get the french out of afficra this way. The down side to this is that the civs you attack get really mad at you and so you wont be able to get a diplomatic win this way. Also you have to maintain a large army to be able to capture the cities of the computer and defend your own.
Doing this will limit the computer form expanding into your territory and you can get a lot of free cities this way. Also attack some of there cities that are already big and have good defensive units. Just take a couple of cities at a time, then sue for peace. This way you chip away at the computer empire slowly. I was able to get the french out of afficra this way. The down side to this is that the civs you attack get really mad at you and so you wont be able to get a diplomatic win this way. Also you have to maintain a large army to be able to capture the cities of the computer and defend your own.