RSmith, NCHillbilly and Dawg2 all know something you don't!!
Coyotes are not as curious to enter a box trap and not to mention that the only way you MIGHT be able to catch one in a box trap is if it did not resemble a box trap but more like a cave or huge dug out hole or something.
I have found coyotes to be extremely wary and the first one I ever caught was the most difficult animal for me to catch after him they came a little easier. I used 1.75 offset jawed steel traps which were modified with 3/16 cold roll as a laminate to widen the area in contact with his foot. I never actually tried to catch one in a live trap so I will not say never but I think he is way to suspicious to enter a wire trap, I am not the best trapper I know but all of the good ones I do know said don't waste your time or money on a live trap.
I would recommend either a good steel trap or snares. While there may not be regulations about trapping coyotes there are about trapping season and about the other species that would be attracted to the same bait as a coyote. If you want to get into trapping I would recommend get some books and videos from most any trapping supply company get familiar with the basics and use this time to scout and if you can get with an experienced trapper (they are getting are to find) to be ready when trapping season comes around.
Dawg,all I ever caught out of mine were dog's,coon's,cat's,and 'possums.I did get rid of the stray dog problem,I had to take them to the county pound.They would not pick them up,because it was hunting land,and not their trap.
Now that everybody has told you that you can't do it, try this. Use a trap big enough to allow a coyote to get in without feeling as if he is walking into something he can't get out of. Drape the trap with camo cloth or use branches and grass to break up the outline of the box. Use tainted meat as bait to draw its attention to your set. Leave the trap outside when not in use and touch it as little as possible, when you do handle it use trappers gloves to avoid getting your scent on it. Check your trap early in the day and check it everyday, do not approach the trap any closer than necessary to see if it has been sprung. Do not be surprised if you catch, coons, possums, cats, dogs and the occaisional fox. I understand that there may be reasons to use a box type trap in certain situations but the old standby 'dirt hole set' using 1 1/2 to size 2 or 2 1/2 steel foot hold traps are by far the better way to go. The traps are less expensive and when you learn how to set them more effective. For more complete information on trapping coyotes, check at trapperman.com, or the trappers education sites for the states of North Dakota, Minnesota, Ohio and North Carolina. The USDA also has an excellent file available on line for nuisance control of many animals here in the south east. If you want more complete info send me a PM and I'll get specific website info for you.
Coyotes are not considered 'Game animals' in the state of Georgia, you may take them by "any legal means" and trapping them is legal. You may wish to check with your regional Game Management office to see if a trapping license is required on your own property but I don't think that it is. There are only 18 regulations concerning trappin in Georgia unlike some states where it runs into a volume of over 200 pages.