Gets a lot easier once you've unlocked the pub/tavern/etc. stuff for places-not-your-starting-provice, which is a few shards into the campaign. There's also a few guards (well, at least one I've seen so far) that boost province mood, though the only one I've seen so far is pretty puny re: defense. You can also just say, "Meh." and slap down a fairly solid guard (patrolmen's my standard, so far, which reduces discontent increase slightly t'boot) and let 'em rebel. You get a hefty discontent drop every time you knock a rebellion attempt down, though I don't think it effects mood any.
Then as mentioned, there's various random events, which can adjust province mood in either direction. Some of those have set results depending on your actions, but... some don't. Watch out for those. You occasionally find blueprints for special buildings you can build (ancient shrine's the one I've seen the most) for a fairly hefty price that have major mood shifting effects, too. Can drop those down on particularly troubled provinces you don't want problems from.
As for the discontent itself, the most common factor seems to be how you conquered the province. Bribing, ferex, almost always causes none while attacking when you can pursue peaceful solutions often cause some (particularly notable with the alliance races, who get pissed.) discontent. One interesting thing I've noticed is that provinces you conquer from your enemies default to quiet when you take over, even if they were a raging rebellion slurry the turn before. It's sometimes a decent enough idea to let your enemy conquer lizard/centaur/whatever provinces along your border and just take 'em from them, if you can manage to do that and keep it.