The TWRA regs are very simple when it comes to hunting coyotes with rifles - the following paragraphs are from the 2005 Tennessee Hunting & Trapping Guide:
Rifles or handguns loaded with center-fire ammunition are prohibited during all deer, bear, or boar seasons for hunting any wildlife except deer, bear, or boar. Coyotes, crows, groundhogs, beaver, feral hogs, foxes and bobcats may be taken by big game hunters while hunting big game with any legal big game weapon or ammunition. (Page 7, Illegal Weapons, #5).
A legal weapon for hunting deer, bear, boar, and feral hogs using centerfire ammo must be .24 caliber or larger, in all counties except where regulated by legislative acts (#2, Deer Bear, Boar and Feral Hog Hunting, page 6).
Essentially, we cannot use firearms using center-fire ammo for hunting beaver, bobcat, coyotes, feral hogs, fox, groundhogs, and crows during during deer, bear or boar seasons (#5 Small Game Hunting, Page 6, '05 Hunting & Trapping Guide).
Rifles or handguns loaded with center-fire ammunition are prohibited for all hunting between 30 minutes after sunset to 30 minutes before sunrise. (Page 7, #4, Illegal Weapons).
Possession of shot larger than No. 4 is prohibited when hunting all wildlife except waterfowl, coyotes, and beaver. (page 6, #4, Ammunition).
Shotguns using ammunition loaded with BBB (0.19 inch diameter) or smaller shot are legal for hunting coyotes and beaver except during big game seasons (Page 6, #2, Small Game Hunting).
Shotguns using ammunition loaded with single solid ball or rifled slugs are legal weapons during deer, bear, boar, and feral hog hunting (Page 6, #1, Deer, Bear, Boar and Feral Hog Hunting).
Oh, and don't forget: The use of predator calls while night hunting any species is prohibited (Page 7, #1, Prohibited Acts). How do we set up and get predators to come to us at night without using a predator call?
So, let's see if I have this right: unless there's a special legislative act for a particular county, during a deer, bear, or boar season we cannot legally hunt coyotes using any caliber center-fire rifle or a shotgun loaded with anything but a single solid ball or rifled slug.
Now, I could hunt coyotes if I lied about being in the act of hunting big game and then legally kill a coyote with a center-fire of .24 caliber or larger or a shotgun loaded with a single solid ball or rifled slug. Course, I'd also have to have the orange and $28 annual big game gun supplemental license, in addition to the $28 combination license. Or fork out the $136 for a sportsman's license. Under these conditions, we have to lie to law enforcement personnel about our intented game animals (if asked) and pay for licenses we don't need for hunting just coyotes.
How much simpler can coyote hunting regulations be in Tennessee?