I'm sorry I'm not sorrier
I'm not sure I know what you mean. What are you sorry for?
I want to say sorry for my partner's bad temper and depressing sense of humor
You don't need to be apologetic for everything. Saying sorry is a good thing but you shouldn't overdo it as it loses its meaning.
How do I do that?
You can take a deeper look at what you are apologizing for and determine if it's something you are willing to change. If you apologize constantly without changing your behavior, the apology will be of less worth.