Re: .22 Rifle Suggestions
My personal favorite dog gun is the 22-250. I would not use a .22 and never use a subsonic. I am sure they will be lethal but i doubt humane.
My main concern would be location. If you are out of town and have a safe shot a 22-250, 223, or any of the smaller hunting calibers would be great. At short range a shotgun would work well, with a good choke #4 buck will hold a lethal pattern for 50yds. or more. As stated before a bow will work, and very well, but perhaps not as quick kill as a firearm.
If you are in city limits you had best make sure anything you do is legal in town. Legal trouble would not be worth a nuisance coyote.
I also agree that they are smart, and if you tickle them with a air rifle, paintball gun or airsoft a few times they are not likely to hang around.
"What we obtain too cheap, we esteem too lightly: it is dearness only that gives every thing its value." Thomas Paine