The offspring of a coyote and a dog will be sterile, incapable of reproduction. Check with any (reputable) biologist on that.
As for the "eastern coyote," unfortunately it's a misnomer that has stuck since we first started seeing them in the late 1960's. I was only 11 years old the first time I saw them, and no one, virtually no one other than my brother who saw them as well (we trapped together), believed me for more than 10 years, when they were widely seen and became an indisputable fact. Today, anyone insisting that they were NOT here would be the one laughed at. Back then, it was me. I began to scour in earnest virtually everything I could find at my disosal in libraries, magazines, etc. I finally found a friend in the NH state biologists office, her name escapes me now, but she took me under her wing and gave me a wealth of information via the mail. Remember, we had no internet back then. But we sure kept the paper companies and the post office busy.
In 1969, part of what she wrote me was that it was her strong opinion that these were in fact no close relation to the "coyotes" of the west; rather, she suspected that they were in fact a distinct subspecies of the red wolf. She taught me a lot, and I've always held what she wrote in the back of my mind, and the more I learned as the years passed by, the more closely my opinions mirrored hers.
Fast-forward to a year ago -- DNA testing of the so-called "eastern coyote" did in fact point to what that good lady suspected all along: These canines are, in fact, more closely related to the red wolf than the coyotes of the west. Unfortunately, the name has stuck, and is now more indelible than our own skin pigmentation. No matter what, they'll always be called coyotes, or worse, "coy-dogs." Sure, coy-dogs are more than mere possibility, but so extraordinarily unlikely that it's not worth discussing. And as for a coy-dog to ever make it to become the alpha male, or female, that would precipitate the demise of the pack, given that, in "eastern coyote" circles, they are the only two of the pack that breed, there would be no offspring, period.
Go ahead and flame away. But I'd sure like to once, just once for a change, have a conversation on this subject without the cloud of ignorance and emotion making a slugfest of the whole thing. I know what I know. It's been nearly 40 years that I've been studying these things, and always far far ahead of the curve of so-called "conventional wisdom" that I'm frequently if not usually mocked and ridiculed for my position(s) on the subject. So you see, whether it was coyotes in the 1960's or turkeys in the late 1970's, or -- well, a whole host of other things that I've been ridiculed for and later proven right (though without any sense of having been vindicated - the folks usually come running to tell me "the news!!!" as though I'd never heard it, or that they'd never heard it from me), the plain facts are just what I've written --- coy-dogs are rare at best and cannot reproduce, and these soyote-creatures that we have are a subspecies of the red wolf. And they DO get quite large at times, though very unlikely that it's any result of interbreeding with domesticated - OR FERAL - dogs. Going wild does NOT change a dogs genetics. At least not in one, or one hundred, generations.
As for hunting them to extermination - we're not that dedicated. Studies have shown that it would take 75% losses sustained for not less than 7-10 years, depending upon pack size and carrying capacity of the land, to truly effect any long-term eradication. Problem is, what number represents 75% of a population that you cannot count? No, the only thing to do is to keep them in check and afraid of man. That brings up another point, the same which was the subject of a Cornell University study on habituation, wherein the authors made it clear that (here in the East, at least) the "coyotes" are at the last stage in their relationship with Man before putting us on their menu. This is remarkable in itself, but made even more disconcerting when viewed in light of the fact that the only other species-wide example that we have of this habit can be found in the polar bear, which routinely figures on humans as part of its prey, whether we agree to it or not.
Anyways, I'm really not sure why I even respond to these debates. They go on everywhere, they are never resolved, and emotion gets the better (and best) of nearly all involved. Fact just can't be separated from fiction. Indeed, fiction becomes fact. And perception of truth matters more than truth itself. All the same, I've laid out what facts and truth I have found, without taint or stain of emotion or ignorance, as best I can. Of course there's more - so much more! -, but --- that's for another time, I figure.