I'd have to agree that anger isn't usually it's own emotion, it's a specific expression of fear or sadness. There are always exceptions I think, but usually there's more to it.
My favorite thing is to express those things through humor. It's not for everybody. If you're not funny enough you can just sound like an idiot or an asshole, as I can. Other times it enables you to attack the root of the problem in a digestible way that doesn't make a person feel attacked.
Steven Universe makes it look so easy