It's not that the 20, "ain't enough" it's that you are limiting your payload and thus your pattern. I'd probably try and shoot #4 buck or BBs and I'd certainly try to find 3" shells. If you get one of those pellets into an important place it'll kill him. The problem is that you have very little control, especially at 40 yards, on where those pellets go.
Since you asked us to be honest, this seems like a stunt to me. I've killed coyotes with a shotgun and I wouldn't try it with a 20 ga or a single shot, but that's just me.