DramaSystem pops into my head here. The main way it works is that one character wants something from another, and they roleplay it out. At the end of a scene, you decide if you got what you wanted, and if so, give up a drama point to the one who granted it.

This doesn’t feel coercive (unless fear of losing a piece of currency can be considered coersion), but there are also mechanics to force them to acquiesce and things like that.