First off, I don't own a .243, and I have no intention to do so, I just felt compelled to add numbers to the end of my name. younggun243.
Catchy,huh?

Anyway, just shoot the coyotes in the head. I saw a photo of a kid that shot a wolf in the face with a .50 cal. muzzleloader, and there was just a hole the size of the bullet. If you shoot the coyotes in the head, you shouldn't have a problem.