J-man
Deity
Once the cities have finished razing the unhappiness from them will go away.
For the Puppets
Garrisons (Military Caste)-> 1 happy
Defense buildings (Professional Army) ->1-4 happy [Puppets will build these at some point]
Culture or Science buildings (Organized Religion or Humanism) -> 1-2 happy, 3 in some [Puppets will build some of these]
Connection (Meritocracy)-> 1 happy
Size 10 + (Aristocracy)-> 1 happy
Courthouses (Police State)->3 happy (but you have to annex them)**** note: courthouses are bugged, you get the +3 happy even without Police state
(Order)-> 1 happy
Specialists (Democracy)->1/2 happy for each [Puppets might run Merchant specialists]
Plus Puppets will naturally build happy buildings if your empire is unhappy
OR you can annex them and force them to build happy buildings (and courthouses)
Thanks for the tips.