Even at very close range, say 25 yards or less, the 22 LR is marginal for a clean kill on a coyote even with reasonable bullet placement IMO. 22 Mag would be some improvement but not that much. There have been a lot of coyotes killed with the 22 LR over the years but there have also been a lot that died a slow death from bullets that did not take out a major artery, the brain or the heart.
To be fair to yourself and the coyote I would suggest you look at something a bit more powerful. The 223 or 17 Remington both do a good job as do many other rounds.
Mike