Dave, it can and DOES happen. I have seen it once. Domestic dogs, wolves, and coyotes all have the same Genus name. They can all successfully breed with each other. Several factors come in to play. When coyotes mate, they both help raise the litter. Obviously not on the domestic dog's list of things to do after breeding. With no help, the survival rate of the hybrid offspring is very low. Also, for a female coyote to allow a domestic to breed her, I would think that there would be no available male coyotes at the time she is in heat.
Just as a roaming domestic female can breed with several domestic male dogs, a coyote can also breed with a domestic, and then a coyote. Thats why you can see several different shapes, sizes, and colors of pups coming from a domestic female that has been bred by several males.

I sent a the picture to a taxidermist friend of mine this morning. I told him there are still some "non-believers" that dogs and coyotes still cross……….He said that just TODAY, he watched as two domestic dogs were on a female coyote, along with a male coyote. He said the big black lab kept the coyote away and also mounted the female coyote……..

That is also why we have two distinct populations of coyote, and they now call ours the "eastern coyote". Thay do in fact have different genetics, closer to our domestic dogs. Our coyotes are bigger, and vary more in color that what the western coyotes do. Thats because the Eastern 1/2 of the county is more populated, has more homesteads and many more individual farms….all with more dogs. The likelihood of a coyote encountering a domestic dog here, is 50 times greater than say one on the plains of Nebraska or on the large ranches of wyoming. Their genetics are more pure coyote, and are what we envision a "coyote" to be and look like.