A controlled expansion deer hunting bullet will usually leave hides very clean in 7-08 (or any other "too big for coyotes" cartridges). If you're a reloader, slow them down a bit, and you can be even more assured of reasonable control. Worst case, you have to throw 30-40 stitches in a hole about the size of a large egg. Hit something hard like the shoulder joint, and it'll push a NASTY wound out the back side. Just keep it far enough back into the soft stuff and you'll be fine.
Throw a light built rapid expansion bullet onto a coyote from a 7-08 and things will get yucky (like winchester ballistic silvertips).