I killed a LOT of coyotes hunting off of horseback in Az with a Ruger 22 Mag and 40g Winchester HP.
My shots were not long as a rule, 75 yards and under they are usually dead right there. As the shots get longer, a direct heart/lung shot is imperative which involves a lot of luck on walking and trotting coyotes.
The Ruger is a 1" grouping rifle at 100 yards on a calm day with the 40g Winchester HP, groups as good with several other bullets but they do not kill worth a hoot. Winchester supreme was not good at dispatching feral cats, must less a coyote.
The key to a coyote 22 mag rifle is to use a bullet that is made to penetrate, and the 50g bullets have terrible trajectory as the distance gets longer...if your gun will shoot them at all(none of mine will shoot them well).
If you use poly tip bullets, expect a lot of run off's...I will not mention brands. Also, some popular bullets do not expand that are copper coated lead and you get a bonus of a leaded up barrel.
Marlin 25M and the Savage Bolt guns are both unreal accurate, but not quite as smooth on feeding as the Ruger. The Marlin Tube feed is my second favorite in the 22 Mag as they feed slick.
If you hit a coyote in the rear of the lung, you may not find him depending on the distance. If you hit him behind the diaphragm, you will for sure NOT find him. So, think like an archer and place your shot.
DO not expect complete penetration or a blood trail.
I use an old beat up Leupold 4x12 Vari-X II with an AO on my Ruger 22 Mag all weather stainless(boat paddle stock).
When shooting a 22 mag, I leade a coyote on the move just like I would using a shotgun, and the Winchester 40g HP will penetrate the shoulder, ribs, and hip joints(running away shots). You have to shoot your rifle a lot and get confidence with it and know the trajectory, and I sight in for 100 yards. My longest shot was a facing shot at 150 yards, I put the cross hair on the top of his head and hit him just below dead center of the chest...he hit the ground fast!