150 yards or less, in a somewhat populated area? Sounds like just the job for the 22 Hornet or better yet, the new 17 Hornet. They will drop any coyote that walks out to those ranges with proper shot placement, and both are relatively 'quiet,' at least compared to other rounds. The 221/222/223 are never a bad choice, but slightly noisier, and you would have to pay more attention to pass-throughs or ricochets. The .17 Remington/.17 Fireball would be fine choices as well.

If you go with one of the Hornet cousins, I would stick with the .17 if you don't reload, if you do, either one would be fine. The .22 Hornet generally needs to be handloaded to bring out its potential; both can be loaded at home significantly cheaper than factory loads.

I would shy away from the 22-250/Swift,WSSM if the ranges are to be relatively close. One would be for pelt preservation, though I am not sure if you are keeping pelts so that may not be an issue. Secondly, because of the proximity to housing.

All in all, I will say that a 17 Hornet would be your best bet for what you are going to ask of it.