Interior Minister

[Tharmas]

I like to bribe my disgruntled leaders but you can't use those cards on the Interior Minister, so over time he/she tends to go down to unacceptable levels. How do you keep you interior minister happy?

[Squarehead]

Good question. It's certainly very useful to have a skilled and especially loyal person as the director of the Interior Council.
The first choice for keeping them happy is simply picking someone whose regime profile preferences generally align with what you are doing with your empire, then the decisions you make each turn should keep their relation high.
If you can't do that it gets tricky. You might be able to pick a loyal person who isn't skilled and then attach an appropriately skilled advisor to them, but then you need to watch out for interpersonal friction between them.
If you are lucky enough to get it the fate stratagem Happy Family will keep the person it is played on happy.
Lastly I think some of the national awards (medal of merit, etc) are played by the Secretary rather than the Interior Minister so they can help in a pinch but suffer from not being repeatable.

[Thrake]

In mng>leader, sort by natural relation level and pick somebody with acceptable skills. Low egoism makes it easier to manage... This is because low egoism is hard/impossible to bribe to increase relations (irrelevant here), however they are more responsive to salary, both the base happiness from salary level and the one-time increase from salary increases. Increasing salary by 1 credit every turn will give a sizeable boost to relations, until the point where it will sit at 100.

Also note that a very impactful factor for leader happiness is word score. Early game it will be low which creates relations issues but over time it should go up and everybody should be easier to deal with. With it at 100 few leaders should actively be not happy so I aim to maximize it as much as possible.

Medal of merit on interior council works indeed, that's a must, beyond the one time boost it's still +1 relations per turn.

[Henoch]

You can try to keep his faction happy which influences his natural relation level. Faction happiness is a very important factor to keep leaders happy. Double check if no attached advisor cause frictions.
For sure leader profile is the key here, if he is not aligned you should consider changing the leader to more aligned one or adjust your profile if more leaders have similar situation.
There are some cards where you can give someone an estate etc. some give permanent relation bonus. You can find the list in the manual:
5.8.9.4. STRATAGEMS TO IMPROVE RELATIONS