but that was so much fun in Civ1! I would always go for an opponents capital as my primary target JUST for that to happen. I think that it could happen if the civ being taken had certain governments, such as despotism, feudal monarchy, or older republics. Because if you remove the central figure, each of the local cheifs is going to want power for themselves.
Anyway, most civil wars have happened in history mainly becuase of a difference in opinion around a single primamry subject matter, be it religion, economics, social upheval, ect. I think that the best way to represent that would be that if your civ is having a lot of civil disorder problems, then that is what should lead to a civil war.
ex. each consecutive turn that your civ has a any city in civil disorder, each the chance of a civil war goes up 1% per city, and each of those cities is remembered by the computer. EX: turn 1: City A is in disorder. At the end of the city report phase of the turn, there is a 1% chance that city A goes into disorder. Turn 2: City A is back in order but B,C,D,E,F go into disorder. Since these were consecutive turns, at the end of the city report phase of turn 2, there is a 6% chance that cities A-F go into rebellion. Turn 3: order restored in all cities but a goes back into disorder. 7% chance that A-F go into rebellion. Turn 4: all order restored. Turn 5: C,F are in disorder, w/ a 2% chance of rebellion since turn 4 saw civil peace.
This can be very difficult to manage if your cities are simply growing and disorder is happening simply because you dont have enough entertainers to workers or what not. So perhaps the culture minister also pays attention to mood and if a city grows during the city report phase to the point where it would go into disorder, then the culture minister promts you with a warning, allowing you to post an entertainer there or increase the luxury rate in that city (which would be nice if each city could have its own rates in relation to a national tax rate), w/o the city having to go into disorder to get your attention.
There should probably also be a maximum of like a 50-75% chance of civil war and a maximum percentage of cities that actually rebel. This would probably lead to much more subversion like there was in Civ2, which is just another name for propoganda.