I can't speak about the dangers to small pets, but I think some of you might be overestimating the likelihood and personal danger of coyote attacks. As a wildlife photographer, I've done the opposite of this advice, many times:
I've jogged behind coyotes, following them until they were in a good spot for photos. I've crawled on my hands and knees within 15-20 feet of a pack, to photograph them. I've stood in front of one from ~12 feet away, for five or more minutes, photographing portraits. (By the way, I would never try to feed one, of course.)
I'm not saying that they are friendly and harmless (and I'm armed, of course), but what I've done was safe enough for me and for the animals, and I will continue to do so.