The .22LR isn't ideal for yotes, but it can work in certain situations.

1. I would limit your shots to 50 yards or less
2. I would take head shots, not chest. Shoot them in the lungs and they'll run forever. Sure, they may die later, but you'll never recover it and it will suffer longer.
3. If you're taking a head shot, make sure the yote is stationary- not running or walking. This is a problem, because in my experience, coyotes keep moving and don't completely stop all that often.

As for ammo, I would use a good quality high or hyper-velocity hollow point- CCI Stingers, Winchester PowerPoints, CCI mini-mag hollowpoints are all good.