TA (most current expansion) isn't actually that much different than DA, from a morale standpoint. Granted, you have 15 less morale on your civ capital (HW) than you do in DA, but that's only a difference of about 1 morale building early on, and less than that later.
I imagine the main thing you need to do is research morale techs, or get morale trade goods-unfortunately, the non-Terran trees are not as good for either of these purposes.
If, however, your experience is from DL, then that may be coloring your perspective significantly-I don't remember much of DL's morale, but it's much harder to have 20B+ populations in DA/TA.
Additionally, what is your taxation rate?
You can, if you like, change the food values for farms, civ capitals, and initial colonies in the xml files, which will lower the population that you have to deal with-but there is no way to change how population decreases morale. I've got a formula around here somewhere if you're interested, but as a general rule of thumb, even with all the morale (not counting buildings) you can expect to get in the game (TA's margin is higher due to extra mining modules), you can't go much over 20B pop a planet at 79% tax without approval going below 20% (at which point you start losing population).
