A 22 would not be my first choice of caliber to take a coyote, but I guess it will work. Just look at all the deer in Indiana that are taken with a 22 each year.
It would probably work if you used one of the higher velocity loads like the Stinger, Supermax, Inteceptor and Velocitor. They will give you he best shot at getting a clean humane kill.
It will work. A well placed shot could kill a coyote at 100yds, although it would be kind of hard to do it in 1 shot. At 25-50yds just light that sucker up. With a 10/22 it should be easy. You could do it with 1 shot to the head or just kind of open fire on the whole thing. During season we spotlight and shoot with a 30 06 150 grain bullet up to 300yds at night.
12,20,.410 slugs work great if you are short on rifles...I've shot coyotes and ground hogs with .410 slugs from an H&R single shot at good yardage...great results!
I'm gonna agree with ggglobert9. A 12 gauge or other shotgun would probably be a better choice at that range. Make sure that you use #6 shot or larger (smaller #=larger shot).
As many have stated a 22 would also not be my first choice for a coyote maybe 223, 22-250 something like that, however, if it is your only option I would upgrade your ammo.
There are several rounds I use for small game, mostly CCI stingers, however I did run across this a while back, however use it as you would see fit
CCI Stinger: 32 grainer @ 1640 fps YouTube - CCI Stinger 32 Gr .22LR JHP - Water Expansion Test (Although I NEVER recommend shooting an unstable surface!!!)
The stinger is faster and smaller, so if your looking for something to punch and creat a larger cavity instead of "beam" through it probly not the best either.
Ok I know you are talking about animals, but more people have died from wounds caused by a .22 then other round. If you take a head shot, 50 yards or in it's game over.
I knew where I was going, how far I'd have to shoot, and it was loaded and hanging above the door when I had a chance to sneak out the back with out the dog tagging along. He was asleep in front of the front door.
Wasn't a big planned out full bore coyote hunt. More of a "just may be..."
I've killed more yotes with a 22lr than I care to count and can only think of maybe 1-2 times where Ive had them run off after being shot. its almost always a kill where they drop instantly or run around in circles for a few seconds before falling over dead. not my preferd cal for yote hunting but if Im hunting where I wont need a shot over 40-50yrds I wont hesitate to bring the 22lr and I always take head shots if I can. if Im hunting a place where I know Ill be setting up in different spots quit a bit and it has alot of open land I bring the 204 ruger or 22-250. and who ever said if you get a head shot with a 22lr your only going to make it mad has never shot a yote in the head with a 22lr. I do suggest using good ammo tho...none of that bulk crap or $1.99 a box stuff. I like the CCI mini mags.