Ships in sector/system do very little for neutral Empires (enemy ships slightly reduce your happiness (0.1%), and friendly ships do nothing at all). Fun eh?
If you are growing quite annoyed with the whole neutral happiness type, the best thing you can do is starting breaking some treaties (it will give you a nice happiness boost) and/or enacting some non-interference treaties. Otherwise, troops, troops and troops are all your rioting worlds need. The UPC should as well to bring these worlds away from rioting, though it will be too weak to improve your happiness beyond Indifferent.
A small edit about UPC and Neutral happiness: the UPC III can be enough to bring a world to Happy for a little while, but will not result in a stable increase in happiness, and would probably not work with a negative happiness characteristic. I believe the natural happiness reduction (going back to Indifferent) happens before UPC (and possibly other events) kick in, which allows to stay on Happy for a turn or two.
So with 100% happiness, and an UPC III, you should expect to stay on the Happy level for 75% of the time, assuming no other event. The problem is, there *will* be other events if you are actually playing, such as winning battles, enacting good treaties, building ships or colonising planets, so you should throw a party whenever one of your planets is Happy without needing troops.
