Use the .308. The coyote won't care at all.
If your primary goal were coyote hunting, that's a whole 'nother deal. There are lots of cartridges which are equally effective as the .308 but with much less recoil. Since that's a secondary goal, however, I wouldn't think twice about it.
I'd use 110-grain loads for coyotes...
You're from BATFE? Come right in! I use all your fine products!