They are here to stay. The proper name is the Eastern Coyote, Canis latrans. Coyotes and dogs theoretically can interbreed to produce what is called a coydog'. In addition, there are behavioral differences between dogs and coyotes which prevent crossbreeding from occurring. Coyotes want to mate with other coyotes and not with dogs.
Coyotes are actually more likely to prey upon a domestic dog instead of mating with it.
It is in this manner that dog genes are prevented from entering the gene pool of true coyotes, maintaining the two separate species. Coydogs occurred at the leading edge of coyote range expansion during the 1950 to early 1970's. The occurrence of a coydog would be an extremely rare event in New York today. Coyote Hunting and Trapping New York hunters and trappers report harvesting over two thousand coyotes each year. All of Upstate New York is open for coyote hunting , a small game hunting license is required.