I know bunch of folks have taken them with .22s, but I like something bigger. The smallest I'd want to use is a .38/.357 in either a handgun or rifle. Weapon of choice would either be my .223, or 7.62x39, but we were talking handguns, so I'm leaving them back home. My favorite hunting handguns are a pair of .44 Bisleys. One is scoped, the other a gold bead/V-notch. Might be a tad overkill on a yote, but that's just what I like to shoot.
That said, however, if I were out in the woods and all I had with me was a .22, and a coyote presented itself with a nice, clean, and close, shot, I'd probably take it.