This is a very incomplete list:

You can improve your reputation by releasing prisoners after battles.

You can lose reputation by:
Starting wars against coreligionists.
Backstabbing your allies.
Cancelling diplomatic agreements (except for when you have to drop an ally due to a declaration of war).
Exterminating cities.
If you give a city to a faction and reconquer it from the same faction.

You get a minor hit from sacking a city, but I can usually keep my "reliable" rep at medium difficulty regardless of that.