Well, there's no need to buy a decoy: a turkey feather tied to a stick will work just as good. Also, in the winter months coyotes are more concerned about keeping their species alive than anything else so a howler or challenge bark call will work the best.
One thing I like to do is get a map of the land and drive around on dirt/log roads the night before. I then use an ambulance siren (on my mp3 player/ipod) which gets them to howl back. I then circle their general location on the map. Once I get a few positions pinpointed I go home and get some rest.
Personally, I would use the .223, but the .22 would work just as good with proper shot placement. The vitals are more or less in the same area of a deer's; the heart is right above the shoulder, and everything is else is right behind it.
Happy hunting, and stay safe!