Gud, given your range your shooting them at, and like you said your hunting in built up areas, that is why I suggested the shotgun, reason being, I am sure you have one, and if you haven't called in any multiples yet you will, using the shotgun you have the piece of mind for safety in your calling area and the ability to dump a double or triple, no way you will pull that off with a rim fire cartridge. I know the noise will be more, but I would rather be safe...
P.S. I use the .223 and the .22-250 for most of my hunting, most of my coyotes end up with entry no exit, but I hand load and use only specific bullets for each gun, I use a 52 grain Speer hollow point for the AR and 50 grain Vmax for 22-250,This is a result of years of experience with terminal ballistic experience on coyotes. Check some of the old threads on the board maybe try a different bullet,I will say I had terrible results with the 55 grain Vmax in my AR, tore the coyotes apart...But other guys love them...