I don't know of any 7mm Mag factory load that won't go through a coyote. I've only shot one with my 7mm Rem. The bullet (160 gr Nosler) entered back of the left shoulder and blew the right shoulder blade through the hide. It was a nice thick January hide. The only way to save what I could was to case skin.
If you handload, Nosler 120 gr Ballistic Tip and Sierra Prohunters are available and might work with a good pile of Reloader 19 behind them.
I appreciate why you like the 7mm and want to use it, but I decided this was a good excuse to buy another gun and save the 7mm for my moose and elk hunts.