Different rules may apply in Virginia than here in Kansas, I thought our whitetails got to be about the same average size...anyway, coyotes don't usually depend on deer for food, and normally won't effect the deer populations at all-of course, out here there's an abundant rabbit/mouse/small game population, if there isn't there, then that may be your problem-I won't say you're wrong, but it usually takes a LOT of effort and energy for coyotes to take down a deer-plus the risk of injury, most coyotes will only try one around here if it's sick, injured, young, or old, but as I mentioned, you don't really notice an effect on deer populations due to coyote predation. Deer and coyotes will often travel the same trails-they shelter in similar areas, they've both got to drink, and where deer eat is likely to be where rabbits eat, so deer and coytes will often sleep in similar areas, then travel to similar feeding areas, so finding tracks together isn't likely to be an indication of a hunt.

If you're just looking to get rid of them no matter what, you've got a lot of options: hunt them, trap them (snares are easiest), put out poisoned meats, or put out word that you're looking for someone to hunt/trap them for you.