I pretty much quit big game hunting 30 yrs ago as my wife now wife doesn't care for game meat or actually much of any meat(she grew up on a farm and worked 10 yrs in a packing house in here youth) so killing a deer or any other big game animal was pretty much a waste. I do hunt ducks any cook them when she is away which is often enough so none go to waist, same with pheasant and quail.
I do hunt coyotes for their pelts in up to 5 different states a year. I will go on an occasional hunt in the fall as part of a predator hunters convention(not a competition hunt). As far as I'm concerned there could be a season on coyotes. Every time I see a summer killed coyote I see $50+ thrown away. I hunt coyotes enough that I have at least a half dozen rifle set up just for coyotes including 3 double guns(combo and drillings)
I do some control work for ranchers but I try hard to do it in the winter, kill a female in Jan. she won't have pups in the spring and you can at least pay for your gas for the trip. Kill her in may and you starve the pups to death and waste the pelt.
Coyotes can be very hard on fawns, Mahuer National Wildlife refuge has been trying for years to reintroduce a native pronghorn population and the coyotes have decimated the yearly fawn crop to the point that the program is making little headway.
16ga/16ga/6.5x58R Sauer 1 oz of NP BB's works well in the shotgun barrel and 90gr Speers sized to .260 in the rifle.
12ga/5.6x50R Mag 1 1/4 oz NP BB's or 52gr Speer HP