I will say that I have followed some coyote (trails) tracks and what they leave behind is devistating. In my area of woods there was massive invasion of coyotes about 4 years ago. A friend of mine and myself harvested 14 coyotes in 3 weekends on a track of around 500 acres.(only 3 of the coyotes were female)We decided that we needed to do something about the population as we found 5 deer, many turkeys, rabbits, ect ect.... 2 of the deer that we foundwere bucks. 1 was a 4 point and the other was a very nice 7 point.

Since the massive slaughter, the woods remained fairly quiet, until this season. We found 3 dead deer and not as much devastation. but I can tell by this sign that they are coming back. There are more tracks out there than there was last year but not nearly as many as there was 4 years ago.

As far as the coyote/ coy dog issue, I have completed 3 years taking biology courses, and will be enrolled for two more years. Although It is not 100% impossible for a coyote to breed with a domesticated dog, there are many factors that will greatly deplete the odds of this occuring. The scientific terms for this is (reproductive barriers) There are many reproductive barriers and they are broken down into two catigories. (PRE ZYGOTIC AND POST ZYGOTIC)

The firstpre zygomatic barrier for example would be called
(TEMPERAL ISOLATION)
Were mating or estrous cycles will occur at different times for land mammals and flowering of plants and flowers will occur at different seasons or times of day.
2nd(HABITAT ISOLATION)
Were populations of a species live in different habitats and do not meet. (this is not a problem with coyote and domestic dog, so this barrier does not apply)
3rd (BEHAVIORAL ISOLATION)
Were there is little or no sexual attraction between different species.

In a scientific study ofa groupsongbirds...scientist took a groupfromone species of birds and seperated them for a period of time. The species of birds were placed in different habitats that caused them to adapt new songs (languages) and some of the birds even adapted new colors for their feathers. The scientist found that when they brought the species back together, that the females were no longer attracted to the males of a different color and the newly adapted language was not understood by the original group of songbirds. This created a new species of songbirds.
( to be considered the same species, it has to be able to reproduce and reproduce with a fertile offspring) like the mule, it is unfertile, making a horse and a donkey (2) seperate species (even though they produced offspring, it was unfertile or sterile)

4th
(MECHANICAL ISOLATION)
Where there is structural differences between genitallia in mammals or flowers preventing copulation of pollen transfer. (this also would not apply to coyotes and dogs in that their genitallia would fit each others)

5th
( GAMETIC ISOLATION)
where male or female gametesdie before uniting or fail to unite
( where egg and sperm will not meet due toa species (males) sperm not surviving in the vaginal canal of another species (female)

POST ZYGOTIC BARRIERS
1st
(HYBRID INVIABILITTY)
where hybrids fail to develop or reach sexual maturity ( like certain diseases of human children where children die at a young age to prevent a population of a new species of humans from forming)

2nd
(HYBRID STERILITY)
where hybrids fail to produce "functional" gametes (like the mule example)

3rd
(HYBRID BREAKDOWN)
where offspring of hybrids are weak or infertile

with all this being said, even if a coyote bred with a dog, the hybrid offspring would not be able to reproduce for itself. In other words (A COYDOG CANNOT PRODUCE ANOTHER COYDOG) so the odds of massive groups of coydogs forming in a small area is highly unlikely, because it is the coming together of dogs and coyotes that can only produce a coydog. Honestly,it would also be unlikely that a dog communicate using the same noises and yelps that a coyote would use (intern making attraction and communication a large reproductive deterant.

A wolf is in the dog family, but it is not the same species as a dog.
A coyote is also related to the dog, but not in the same species.
however, a doberman pincher is a dog and so is a german shepperd, therefore allowing them to produce fertile offspring.( Although they look entirely different, they can still breed "BECAUSE THEY ARE THE SAME SPECIES"A dog that is a (mut) can breed and produce pups.
However,a coyote that breeds with a dog...produces a coydog that cannot breed with another dog or coyote and produce nothing. This indeed makes a population of (coy dogs) harder to come by.