I know each locale is different, but I am not convinced that coyotes are a big factor in MY area (Pocono region of PA) for the predation of GH's or even deer. At our hunting camp I have several trail cams monitoring a 5 acre food plot. We didn't have GH's until we bulldozed high mounds for backstops at various ranges, and then they moved in -so much so that each berm had it's own resident in short order as well as dens along the fence rows. Our range is used by the local police Tactical team and they occasionally will take one as well as some club members. The cameras are out 24/7 365 and this is the first time in recent years that I have a pic of a coyote leaving the field with a GH. Typically I get pics of coyote and fox about every other night (very rarely in daylight) and the occasional bobcat and fisher. Bears all the time. Only ever had one pack of coyotes on cam, always a single or a pair. And with all this, including hawks who are regular visitors, we still have rabbits.
Down at home, I have farmed fields amongst a few other houses, and see / hear coyotes, regularly at dusk/ dawn. I have always (and still do) had GH's in my fence rows, under outbuildings, and adjacent fallow fields. But I do not feel comfortable to shoot (although not prohibited by twsp. ordinances) in any direction due to proximity of heavily traveled state and township roads and the land is very flat. Deer have found a home in the small (2-3 acre) woodlot/swamp patches and I can observe them almost nightly in the field behind my house. Their only threat is vehicles. In the farmland across the road where I used to do my GH hunting before a few houses were put in, that farmer uses gas to control them and it proves very effective.
Perhaps there are so many roadkills here to satisfy the coyotes as evidenced by the ass end being eaten out overnight, that it is more lucrative than chasing the deer down.