17hmr would be you best bet but it's still loud enough to require protection and marginal for coyotes at 150 yards.
The gun you have is better. Keep a set of muffs near the gun or ammo. If the critter is gone because you stopped to wear ear protection, is killing it really that important?
Still happily answering to the call-sign Peetza.
The problem, as you so eloquently put it, is choice.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.