I shortly contemplated the idea of bringing back expansion civics as a way to interact with stability more directly but in the end I couldn't come up with enough concepts to fill a column, which is a good sign that it'd be a bad idea.
Surely there must be enough to fill it?
1. None
2. Satrapy - Half stability penalties for occupying foreign cores
3. Vassalage - +3 stability points for each vassal
4. Centalisation - Core population counts 50% extra in stability checks (stacks well with proposed Absolutism bonus)
5. Resettlement - All cities founded on other continents count as being historical territory for population purposes
6. Occupation - No stability penalties from cities under occupation and population of conquered cities counted as historical territory
With Totalitarianism replacing Imperialism. By the time you get Totalitarianism, Satrapy will be outdated so there's unlikely to be a stacking effect there.
EDIT: Another alternative is Isolationism (or a better name) - No stability penalties (or half penalties) for poor foreign relations. Helps avoid the problem of AIs DOWing on you then refusing to talk, leaving you stuck with a penalty you can't remove for at least 10 turns.