The bullet is only part of the equation to not ruining a pelt. The biggest is shot placement. Shooting a coyote with a frontal chest shot very rarely leaves anything other than a small. hole. Any broadside shot that hits bone is asking for a big hole. Usually you can wait a coyote out to get the best shot placement. Granted you can shoot a bigger heavier bullet and get a slightly less chance of a big hole but only if the shot placement is right on the money and you lose a tremendous advantage of bullet speed which translates into less lead on a runner and less holdover on longer distances. If you want to snipe them at over 600 yrds then a heavier bullet would make sense.
I use 55gr to 70gr out of my .243 WSSM at speeds from 3760 to 4100 fps, a 65 gr out of my .243
a 50 or 52 gr out of a .24 is a good choice. The 52 gr speer with the large HP is a good one for a .223 out to 200 yrds or so. Hope this helps.