VH,
My dad used some "subsonic" 22 shells to fix a similar situation a few years back. Not as powerful as a deer rifle, of course, but with a well-placed shot, you might keep from scaring the heck out of your neighbors with a midnight boom.
Not that I'm suggesting that killing it is the best, or only, option. . . but if it comes to it, you might give those a "shot."
P.S. Rabies is REAL and is not something you want to mess around with. Coyotes are known carriers and should be assumed "rabid" until proven otherwise by laboratory testing. If you or anyone else gets bitten, tell your doctor immediately. And, if you do kill the thing, wear protective gear and a mask when disposing of the carcass.