The only ethical way to use a .22lr on anything bigger than a rabbit is a brain shot with a solid. I lived in Africa for some years and use to carry a .22 pump loaded with solids because it was a pretty good meat gun. I would only take shots at less than about 40 yards when the critter was stopped and I had a stable rest and could be sure to put the shot either between the eyes front on or between the eye and ear from the side. And the biggest animals I shot were warthogs, up to maybe 75lbs. If the shot was good they'd drop like a rock. If it wasn't, they took off and you'd never find them. For birds, I always aimed for the head. You either hit them or you didn't. I'm fairly confident that a deer shot accurately in the head would drop just as reliably, but that's not an option here in NA, and rightly so.
Before I moved over there, I used to use a .22 a lot for hunting, mostly groundhogs and rabbits. I found the Stingers were not very reliable on groundhogs because the bullets were lightly constructed and came apart quickly without much penetration. They will kill a rabbit pretty quickly with a chest shot but do a lot of damage. IMO, the only way you could count on killing a coyote with a .22 of any sort would be a headshot, and if you're taking those, there's no advantage to using Stingers. The bullets are 32 grain HPs. If you can't count on a bullet killing reliably, you shouldn't use it. On a coyote, you can't count on a reliable kill. And as someone else said, Stingers are just not very accurate, which on small game that require fairly surgical shots, matters.