I like to use a Winchester model 70 in .243 with an 80 grain Hornady PSP going out about 3,200 fps. Dramatic when you connect with one of those brush wolves!
I think shooting coyotes is definitely sporting - and fun with a purpose. When my late grandfather was a sprout (in the 1920's in DeLeon, Texas), coyotes were considered animated practice targets.
A young boy was thought a very poor shot indeed, if he could not hit a bully taw marble from 80 yards (open sights) with a .22 cal. Coyotes provided a way for the boys to hone their marksmanship - as was also true of rats and ground squirrels.
Is it any wonder that his generation of men and boys from the middle of the continent often became the lethally skilled snipers of WWII in the islands of the Pacific, and the cities and countryside villages of Europe?
Though stricken with polio in his childhood, even at 75, "old granddad" could still hold a 5" diameter pattern of 8 shots from 100 yards - open sights with his eyeglasses on..
MY favorite coyote expedition - a few years ago while deer hunting in the Oregon Coast Range mountains, I spied a mangy little coyote traipsing down a logging road about 180 yards distant, and moving away. I had 2 rifles with me, so I popped off 3 shots from my semiauto .22 cal. (open sights) at the dirt about 10 and 5 yards in front of him, to stop/redirect him. He stopped, turned around, took a quick dump, and then presented me with a perfect broadside target.
I set aside the .22, picked up my .30-.30, loaded with 165gr. Nosler partitions, slid the bolt into place, and took a quick peep through the old Weaver brass duplex scope before squeezing the shot off.
Placement was so completely perfect, the Nosler virtually gutted the pest for me, spraying his innards evenly over a wild hazelnut shrub behind him. All I had to do was cuff and cape the hide. He never felt a thing after the initial THUMP!
In 13 years of hunting, I've taken down 9 deer (1 mule, 8 blacktail) - all on a single shots - 8 no further away than 60 yards, 1 from 150. All were dead and gone within less than 3 minutes of getting hit. I have taken countless rabbits, coyotes, and other small game, as well as shotgunning game birds with similar outcome. Every hunter worth their salt wants such results. We are part of a normal chain in nature, and have respect for our roles.
My point - and I do have one - no wild animal ever met a less cruel fate in the desert or forest than at the mercy of my bullet - or that of my ethical fellow hunters. Their choices in the wild are pretty much limited - die of starvation, die of disease/malnutrition, die of a natural disaster (like a flood or the eruption of Mt St. Helens), die of painful old age , or die at the teeth and claws of another superior predator.
The deer population here in Oregon vastly exceeds that of Maine on a per acre and a total basis. This should not be.
We have innumerable coyotes, though they are hunted year around. We also - as ColdHeart mentioned have an enviro- extremist engineered moratorium on hunting bears - and cougars with dogs or bait stations. If you can't find and kill these furtive predators on your own - well you're pretty much screwed...it is just a matter of "accident".
As a direct result, both populations are skyrocketing - some would say out of control. Bear/human contacts are routine now - fortunately our little black bears are not agressive - usually. Cougar/human contacts are also up significantly.
Seven years ago, living with my ex wife in Gresham, Oregon a Portland suburb of 90,000, my 8 year old stepson came home from grade school telling me, "We had a cougar at school today, Daddy." I initially thought he meant a stuffed, mounted specimen brought by someone else's dad.
No, right in suburbia, walked a 3/4 grown young male cougar. Seen by a school secretary, the cat was walking in the breezeway entry (where schoolbuses offloaded in front of the school)10 minutes after the last bus emptied, exhibiting what I know to be stage 3 stalking behavior - walking in smaller circles, sniffing the air, head moving side to side...Police later treed the animal in a back yard, shot killed, and autopsied it. The remains of 3 housecats were found in the stomach of the 130lb predator.
Varmints spread disease, predators spread fear. Coyotes are both. The enviro-geeks are idealistic, naive and clueless (except where they are in leadership and operate from a deeper political agenda of trying to gain socialistic control), and they have no place setting public policy.