When you go conquer a city, always make sure to keep a couple of soldier companies in your city. This serves a dual function...
1.You will not face opportunistic attacks from other rivals thinking that you are weak.
2.It will keep freshly conquered vassals from rebelling the moment you conquer them...because their logic works the same way as other rivals.If you conquer them but have no troops in your city, they think you weak and rebel. And a large gift of any sort, especially something they buy will help improve their mood.
Hope this helps.