Place (1) Urban Pacification Center in each system you capture. This will help keep your captured planet populations happy for the long term. It'll also allow you to move your Troops in and out of the system much faster then having to leave them on a particular planet for a set number of turns.
If you've never used Urban Centers then you'll need at least (1) non-Angry world to build the Facility on. But once you have it, all your problems will go away
