If you're looking for a rifle at night, one popular suggestion on the site I mentioned in my first post is the .17 remington or .17 fireball.
And for coyote specific shotgun loads:
(b) during the hours from ½ hour after sunset to ½ hour before sunrise, handguns are restricted to those chambered not larger than .38 caliber, and rifles to those chambered not larger than .22 long rifle;
Based on that I think the Fireball is out as it's a center fire round, by this interpretation the .22 WMR rim fire might be illegal as well. Its hard to tell if the law means rim fire only after hours or anything smaller than. I might call DCR on this one.
The hevi shot was what I was thinking of, 3.5" shells and has a picture of a coyote on the box. $30+ for a box of shells if I remember right.