Houses are a source of disaproval
mines too
and outposts
Loosing units too, you can burn the dead to recover the lost approval.

Vineyards give 10 approval but take 10 if destroyed.
Vigil give approval when its under 0 and will fight rebels automatically, when a vigil kill a rebel you gain approval.
Temple gives approval and got abilities that can help recover it.
Government adds new values and ways to deal with approval.
The wrestling building gives approval. The racing stadium can organise races that give approval.
The cabin is like a farm and a vineyard in one.

Always try to keep approval over 0
you get lots of problems under 0
at -25, mines stop working (-50 for slave mines). -40, rebels attacks in small bands. -50, Pottery stop working. -80, you're screwed a big army will attack you until you're dead or you get back over -80.

When you plan a big fight, sacrifice to Hades to gain approval and loose fear of the gods with each kill. Sacrifice to Poseidon before sending troops at sea and while they are at sea. Sacrifice to Zeus to remove fear of the gods and gain some approval.

Oligarchy can banish Aristois from Estates to gain approval, the more banished, the more recovered.

Democracy can start a long debate that will restore approval based on its current value.

Monarchy can force the rebels to attack and get back to 100 approval. You need an army to defend yourself.

If you know all this, you shouldn't have much approval problems anymore.

I hope it helps and you learned new tricks.