What's the best way(s) to keep my population happy?

Researching Xeno Entertainment and building Harmony Crystals are the best. Yellow mining resources and Ultra Spices are also good. Be sure you're upgrading those entertainment centers to multimedia centers, extreme stadia, etc.. The bonus from ent. centers isn't that big.

High population is the main cause of low morale, and an easy mistake is to build too many farms. Most of my planets have no farm, my economy specialized planets have one farm, and only an economy planet with really high PQ would have two farms. The planets with farms need an equal number of entertainment buildings. Keeping population low lets you keep morale and tax rate high.

don't exceed 19 billion people on your planets. you can build one of the most advanced farms on a world, or two of the second-most advanced forms on each world, to avoid this milestone. also keep in mind you civilization capital produces more food innately.

Mine those Morale boosting resources as soon as you find one that has not been claimed. Never build more than 2 farms on a planet. Do not build on any tiles with population bonuses until you can develop more advanced forms of entertainment to make your people happy.

Research technologies that improves your moral and allows you to build entertainment structures. These technologies usually begin with the word "Xeno". Build those trade good that will boost your morale when they become available like: Frictionless Clothing, Harmony Crystals, and Ultra Spices.

A little advance planning will help out after the normal booze and loose women stop.

Best Rule is keep your populations down low.

My Rule of Thumb- Keep only one farm per planet unless you want to be building more entertainment centers on them. I find this is a waste of a good tile on the normal planets. Dont build farms on tiles that have more then the 100% bonus. A 300% tile for farming ballons up your population way to high once you start upgrading your farming tiles.

I find that once I start getting over 15mil in pop my moral starts going to crap on that planet unless I start building additional entertainment structures. I find it easier just to keep the pop down as it grows faster then I can use it for the most part.

Watch your tax rate. Overtaxing will pissoff the general population (I know I am not to fond of it myself). I try and keep things around 75% approval. Anything lower and some of the higher pop planets start slipping in moral unless you build more entertainment centers on them (again a waste of a good tile).

Put population in cold storage for later use (create fleets of transports off world). I like making a 5bill pop transport with lots of engines. It will usually take out a planet and still leave enough that the planet semi protected from a counter strike.