I recommend getting a road runner and things will work out. Somehow that pesky coyote will get his in the end.
Seriously, don't go shooting it. It is illegal to discharge a firearm where you live. You could also be charged with negligent discharge of a firearm. Not worth it. Just keep your dog/animals inside. I would bet that once it figures out there is no food to be had it will move on. If that fails, call the ACME Corporation and order some anvils, dynamite, and maybe a catapult. Good luck!