The only way to quickly end the rioting is to end the war. Wars in republic, especially if initiated by you, must be quick and hard. Things that help war weariness are:
1. Upping the luxury budget. Is an expensive way to fight WW, but sometimes necessary when it has gotten far.
2. Entertainers. IMHO good for cities that riot before all the others do, e.g. outside of the "main riot wave".
3. Luxuries should be hooked up. If you're fighting for them, hook them up ASAP. Build marketplaces to increase their effectiveness.
4. Universal Suffrage, though not very applicable right now (in the musketmen age, I mean).
The main rule is to have the war won before it even starts. That way there won't have to be a long, drawn out war. The worst kind is one that you initiate without proper preparation. You run the risk of fighting a war in the midst of your own cities, one that you perhaps cannot get out of because the AI won't recognize your begs for peace. I made that critical error in my current game a while ago... I was planning to get rid of the Byzantines, and took my chance when Portugal (being the world dominant power) declared war on them. I was hopelessly unprepared, and Portugal was unable to make too much of a difference. I ended up having to fight on my own lands, and bringing an AI invasion under control is really difficult if you lose control. War weariness was running amok, and I had to shut down all research for 8-9 turns to pay for the lux budget. It was really dim until I finally brought the invasion under control and managed to get peace. Bleh, I'm diverging.
