Hmmm... Karamojo Bell killed an elephant (!) using the .22 LR in a Colt Woodsman. No one is pushing the .22 over the .458 for an elephant cartridge.
Sure... you can KILL a coyote with a .22 LR. Any coyote you shoot through the chest with a .22 will almost certainly die. The problem is, it might take a while.
If everything goes just right... if the coyote is close enough, if the bullet slips through the ribs, if the bullet or a bone fragment hits the aorta or the liver or the spine... sure, you'll stop it in it's tracks. That's a lot of 'ifs.' A cartridge suitable for a varmint species will almost certainly drop it in its tracks with a broadside chest shot... and the .22 LR won't do that.
All of the Velociraptors, Quik Shots, etc., won't make a silk purse out of the .22 LR. It just isn't powerful enough for consistent quick kills on coyote.