Rick Perry is almost assuredly carrying the extremely popular Ruger LCP:
http://www.gunblast.com/images/Ruger-LCP/DSC03240.jpg
Reliable ultra compact pistols, or pocket pistols, are a very recent phenomenon. Obtaining a LCP was very difficult for the last few years as Ruger couldn't manufacture them fast enough to meet demand. If one were to run with one, it would hardly be noticeable. There are no sights to speak of and it is not accurate at distances beyond 10 feet with or without a laser, which many Ruger LCP's have on the grip. The coyote would have to be very close for Perry to have put it down in one shot.