I have killed a bobcat (and only one) with a .204 and 40 grain Vmax. Didn't blow it up at all.
Side view after it had ridden around in the truck for a while.
.22 Mag Foxes. 30 grain Speer TNT
A pair of foxes with a .204 and 40 grain Bergers. Hit low in the chest on the top one and it was wrecked a little bit.
Hope that helps. I have seen plenty of coyotes fall to the combinations above, but I have seen plenty run off as well. If there is a chance you would want to shoot a coyote on the same hunt, I would use a .204 with 35 or 40 grain Bergers as a minimum.
.17's seem to be the hot ticket, but I have no experience with them. I might build a .17/204 so I can find out....