I have shot a bunch of ground hogs, and a few coyotes with the 223 cartridge. I do not have enough experience on coyotes to give a trusted answer, but I can attest to what the cartridge will do to WV, PA, and MD groundhogs.
These ground hogs are pretty tough critters, and it takes a good solid hit to anchor them.
First off I detest crawl offs, so my ranges are limited to what I consider are humane distances to anchor a ground hog. I limit my shots to 300 yards with a bolt action rifle. I do shoot many out to 400 yards with my RR AR, however I always deliver a very fast follow up shot to anchor the animal.
The cartridge wil kill at longer distances, no doubt. However you wil run the risk of crawl offs, and I do not do that. Tom.