Policies are one of my favorite ways to keep up with happiness. It doesn't matter what kind of game I play anymore, I always try and focus at least moderately on culture. One of the Key ones I go for almost every time I play is Protectionism in the commerce Branch which gives you +1 per Lux resource. With 5 or less cities I would focus heavily on Pop. in my capital and also go for Tradition to Monarchy. Then, aside from that I'd just follow the other suggestions everyone has made; Happiness buildings, as many Lux Resources as you can, trade lots, buy CS's, some Wonders can be Key as well.
I find the bigger games I play the more it causes a huge Boost of hapiness at various points in the game. E.G I recently played Arabia on a Huge map, standard length on King Difficulty, I was playing a 'Monger from the start taking Polynesia and Pachacuti out before 0A.D, which was challenging and fun because they each had UU for that era. I had 2 such boosts during the game, Once when I reached Protectionism, I already had 15+ resources and BAM huge happiness increase. Second happened once I reached police state, I had a boost of over 60 Happiness at one time because I had built over 20 courthouses to keep up with unhappiness until that point.