Coyotes always have and always will take a tally on the deer herds and it usually happens during the spring when the doe's are dropping their fawns. 

As far as shooting one when I see it, I will try my best when ever I see a coyote out in the hills but when you just chance onto one they are usually already aware of you and offer a real fast moving target.  But come winter time they come into a call quite easly so I try and do my part to get rid of a few of them each year.  My primary weapon in a Ithica Mag 10 ga shotgun loaded with some 0000 buck shot.  If I feel sporting I will use my .22-250 when they are between 100 and 400 yards out. 

Good work Critter... we shoot them too.

A lot of guys hunt them - I just shoot them when I see them from the deer stands.

Here in the east we see them pretty often - many times at less than 100 yards

The coyotes are around here but aren't very thick innumbers. We see them every once in a while but we are hearing them more often. So the sitings should also increase.
Whenever we see them, we'll shoot them. We don't feel we have enough of a year around, resident population to call them in on a regular basis. Coyote hunting around here is a by-product of deer or turkey hunting. More coyotes are caught while trapping than shot while hunting. They seem to be wondering through at different times of the year, no daily sightings or hearing them.
It's funny you bring up the insurance industry and the decline of the deer population. They, the insurance industry, successfully lobbied to have the doe deer season extended in part of eastern NC.
As far as how much damage they can inflict upon a deer herd, it would be difficult to measure. There has been studies dine that show coyotes will take 1 or more fawns from a given herd per day during the time in which fawns are dropped. Not to mention the destruction they cause to other animals such as turkeys and their nests.
They definitely need to be kept in check.

ECU - we have lots of them down here - they are flat spooky at night when they howl... at times, we howl at them and that will get them started.

For as many of them as there are - and as seldom as we see them - they are one more super smart dog....

You are sure right about insurence companies wanting a much smaller deer population. The numbers of deer vs. vehicle collisions out east always boggles my mind. It is amazing how many deer you guys have. But I can see why you do not want a drastically smaller herd and why you might be a little defensive when it comes to giving up your deer to coyotes. I take a moderate stand on the issue. I am not going to stand here and say that I do not have any problems with coyotes really hammering a deer herd. I am an animal... a hunter... a predator. I have competition in the form of other predators. All species have always tried to outcompete (excuse the anthropamorphism) their competitors so yes... I don't like to see them decimate deer herds. But they fill an important niche in the ecosystem and have done so for a long time. I do not want to see every coyote killed in order to boost deer numbers but I have no problem trying to control their numbers. The problem is that they are a species that responds readily to hunting. The more you kill the more they pump out.

I am not doubting you Jim, I am just a little suspicious about their research, and the fact that they attribute that big a decline to coyotes.  Coyotes are not wolves.  The main way the coyotes get deer is when they are weak, injured, or when environmental factors are a contributer.  When the snow get's deep, or icy, and the Coyotes can walk on top of it, they get alot of deer.

A healthy whitetail adult can outrun and outsmart any coyote, hands down. The coyotes possibly could target the fawns, but seriously, a 30% decline due to this???  I'd be loooking at other factors too.