The fastest way to get them to stop is to drop troops on the planet in question. "Be happy... or else!"
Planets will also get happy from having ships in the system and in orbit, but its obviously more expensive. A good short term measure, though.
Once the people are back in line, you can have them build Urban Pacification Centers, which improve happiness in the entire system. You'll get them by researching Applied Political Science.
One major cause of riots is a bad initial choice for your people's happiness type.
If you chose Bloodthirsty, your people will get upset when you sign treaties with aliens, and get happier when you declare wars and kill things.
If your people are "Neutral", then they get upset at just about anything. Treaties, wars, new colonies even. They calm down faster than normal, but they are generally considered the hardest happiness type to deal with.