What exactly is the mechanics of gaining/losing money for protector/protectorat

[Bactron]

If you are not able to gain protectorates. Then listen up.
You both should try Forced diplomacy minimod. It's really good option since the normal diplomacy is quite bad. And if you make some house-rules and will not abuse it then it is really good thing.

I for example use it but only with these rules - I must have a large and powerful empire in order to make someone my protectorate. The enemy has to suffer lots of defeats from me, and that faction has to have only one or two remaining provinces, then I usually send a full stack/s to (both)their remaining province/s I march right next to their cities. And then I use a force diplomacy to make them to accept it.