Aggressors: Ancient Rome – Why Is My City in Revolt?
There could be several reasons for this and it is worth reading the pop up windows to find the root of the problem. Cities are often in revolt when the local happiness is too low, which means people are unhappy. Reasons for this can be found in the Resource usage map in Happiness tab. Hovering over the particular city shows the major factors affecting local happiness.
Another reason for a city to revolt is that another state is spreading its influence there (if this is the case, you will be notified by a pop up window).
If it is a newly conquered city, it is quite likely that the rebellions are caused by low Loyalty and General Morale levels. You can see both in the Unit menu when you click on the city in question.
You can mitigate the risk of rebellions in your cities by building improvements (e.g. Civil service, Obedience), keeping a garrison unit (urban guard) in the city and advancing the front or agreeing on peace terms with the enemy on your borders.