I've shot numerous coyotes with my K98 heavy barrel 308 during the course of deer hunting. Damage isn't too much worse than my Stevens 223. I had a 62 gr FMJ 223 clip a rib last year and blow a hole big enough to put my head in out the other side of the hide. Never seen anything like that before. I nailed my first yote with archery tackle last year and took what I consider to be one of my best (or luckiest) shots ever on a running yote at 125 yds with my Thompson Centre muzzleloader a couple seasons ago.
Back to the original question, I have a war dated, swastica'ed K 98 action that at some point ended up with a heavy 308 bull barrel on it. We put it in a vintage sporter stock and glass bedded it. Nicknamed the fence post, it can be a little heavy for all day walking. That's why the 223 is the go to varmint rifle these days.