I think that the potential for rebellions is a good idea, but that it greatly depends on your form of government, interaction with the people, and composition of your people.
Composition:
If you have conquered another civ or a large portion of another civ, then foreign residents are more likely to rebel. This would be a way to encourage conquering a another civ, but then setting up a friendly government in it. You lose the threat, gain an ally, but dont have the concern of keeping conquered citizens happy. This would also represent unfortunate rationale for ethnic cleansing that has dogged civilization since its beginnings.
Interaction:
(1) Between Cities-Keeping cities in social contact is crucial. If a city(cities) is disconnected from your national trade network for an extended period of time, this could represent these cities losing touch w/ the rest of your civ and developing their own nationality.
(2) W/ your people-Maybe make civil disorder more of a threat than it currently is. Somehow tie civil disorder into the chance of cities breaking off and forming another civ. Ex: If a certian group of cities keeps going into disorder simply from poor management, they may break off.
Government:
A chiefdom or feudal monarchy is more likely to have rebellions that try to break off than a more central government. Each is merely an alliance, with the leader usually assigned by military might or charisma, w/ frequent internal squabbles. Now, yes the US had a Civil war. But, that was brought about by ideological differences. Those differences happened because a different social and economic conditions between the north and south. Perhaps that can be reflected in the game by what improvements a city has. If a city has mostly scientific improvements, then it's citizens may have different philosopies and values than a city w/ mostly industrious improvements. This philisophical difference could promote a civil war, like it did for the US. This would encourage players to diversify their cities' improvements, rather than have cities that exists for specific tasks.
I loved the capture of a capitol creates civil war ploy in Civ1. But I think that should again depend on above conditions of the Civ whose capitol you just captured. If someone has a very unified civ, then the capture of its capitol wont break it up, rather the opposite: create a nationalistic fever, making the civ not rest until it retakes its capitol or other variables. But if you capture a capitol of a civ that is falling victim (or close to it) to the symptoms above, then the chances of civil war are much greater. But that doesnt always mean that one side will like you. They may still want their capitol back, creating a 3-way war!