I have shot alot of coyotes with my 243, and once I found the 60gr Sierra HP the damage went away. I actually wreck less furs with that load than my 223s do. As long as you don't hit a major bone 90% of the dogs I've shot with my 243 you can't even see a hole, alot of them don't even make blood on the snow. I have those lil bullets cranking at 3600fps.
I've also shot alot of dogs with 95gr Combined Technology BTs and as long as you stay away from shoulder blades I only get about 1-1.5" exit holes.