[Still Thinking]

Something in the .223 (or 5.56), .243, or .270 range would probably be the cheapest that would get you quick kills. These do represent a danger to neighbors though as the rounds can kill out to about 600 yds and will travel 1 1/2 miles.

A .22 would kill them but not quickly unless you can get within 75 yds and are good enough for a headshot.

How about a 22 Hornet? About 4 times the energy of a 22 LR, but half or so of the normal full-size small centerfires. Even a 22 WinMag would be a step up from a 22 LR. I'd think that'd give you more range on the coyotes but still be safer for the neighbors.

[driftdiver]

It would probably do the job, all depends on accuracy. I killed a 30-40 pound porcupine with a 22LR and it dropped like a rock, however I was able to get a clear headshot.

22mags are used to kill cows at the slaughterhouse in some places. So they’ll do the job, if you hit them right.