Hi Jon,
Welcome to the forum! I also spend a lot of time in the woods, with the bulk of the time being in Northern Mercer and Hunterdon Counties, in areas where there are a lot of coyote. I've never seen one but have heard them and have seen plenty of sign to let me know that they are present, and in one or two cases they were present in large numbers. My direct experience agrees with that of others on here, I've never had a problem. I am not trying to invalidate your concern, however statistically your chances are very small that you will be bothered. Consider, foremost, that there is plenty of prey for the coyotes here (everything from rodents to deer), so the coyotes are well-fed and likely content. I would worry more if the coyote population exploded to the point where they were being pushed outside of their natural habitats because of a decline in food, because I think that human habituation is the major precursor to the problems that could arise with coyote.
I'd be lying if I said that I am not concerned at times too. I'm not sure that everyone shakes the natural skittishness that they may have about the possibility of running into bear or coyote. It's a natural, visceral fear, and that's why it resonates the way it does. Sometimes when hiking alone I still look twice behind me, and random noises such as deer scampering through the brush can still bring my heart rate up. That being said, my best recommendation is to not make yourself so anxious as to not enjoy your time in the woods. If carrying bear spray helps, do so. I've heard that an air horn can be good, others recommend awareness, ability to bluff, and a good-sized stick. I do carry spray, for the record.
I recommend getting a book or two on mammal signs and behavior. I strongly believe that when someone fears an animal, fascination is not far behind. The Stokes guide to Animal Tracking and Behavior is a very good book, a bit light on the tracking but a home run on the behavior end, and Len McDougall has a great tracking book that is a terrific balance of tracking, behavior and natural history. I realize that not everyone has the time to plop down with a book about animal behavior, but I think that understanding a predator's natural history and behavior deepens our experiences with them, and lends a facet other than anxiety to hearing them or seeing signs of them in our presence.
Enjoy your time in the pines!
Chilehead