I use a .25cal Air Force Condor SS. In Az, it has to be .22 or over pre-charged, but over .30 they treat it like a firearm and you can't discharge it within 1/4 mile of an occupied building.
Like Chupa said, most of the bigger air guns are using actual bullets. Pellets do have issues with lack of expansion, but you are packing enough energy for a good head shot where expansion is not such an issue. My Condor pushes a 27gr, .25cal pellet at 950 fps which is similar ballistically to a #4 buckshot pellet. Broadside headshots work great. Head on headshots might be a bit dicey especially on a coyote if you hit the face/brow area. Top of the head, no problem.
Shot placement is critical, but these air rifles are so accurate that it really isn't that bad. you just have to get them lined up. 20-40 yards and you are good to go, you just have to be a bit more selective about which shots to take.