rookie
I whole heartedly agree with lawdog, i've shot coyotes up close and personal with everything from a 17HMR to a 338 win mag. and the 22lr just isn't enough gun, the head or rather the brain of a coyote is about the size of a small mandarin orange, I'm sure you can hit a orange at 70 yds but remember that orange is now hidden behind eyes, ears, jaws, and fur and is moving around up, down, side to side and to top it all off you'll probably be excited and maybe not shooting at your best and for sure not from a bench or at least a steady rest. And as for body shots, I've seen coyotes run flat out 300 or more yards after a solid lung hit with a 22LR likly this was in a full half section field with no trees so it was recovered. I think lawdogs got it right a NEF 22 hornet or HR topper in .223 can't be that expensive down there in the states up here in Canada they only run around $300CAN.
but regardless of what you choose good luck, please respect the animal, other outdoor enthusiaists and the land owners . and for sure have fun.