We grill our turkey for thanksgiving every year. Super simple and EXTREMELY flavorful. I think the original recipe came from the Weber cookbook.
Get 50 coals going in the Weber. Once they start to grey, spread them out to the edge and put a drip pan in the center. Slather your bird with PEANUT OIL (do not use any other type). Salt (Kosher) & pepper the bird inside and out. Tuck some onion, celery and carrot in the cavity. Truss the legs and wings. Put foil on the wing tips. Slap that baby on the grill, breast side up. Open ALL of the vents and cover. After about 45 minutes or so (when the coals have started to die, add 25 more briquettes Check for doneness at about 1.5 hours.
Depending on the outside temperature, I've had 14# birds done in 1.5 hours on warm days all the way to 3 hours on freezing days.
I've used a Weber kettle for years and it does a great bird.
1) Brine it. Not too much sugar or apple juice in the brine or the skin may burn. The basic Alton Brown foodnetwork thing works great.
2) Set up two fires in the kettle with a strong alumunum drip pan in the middle.
3) Prepare an aluminum foil breast covering to place on the bird after the 1st hour of cooking.
4) No stuffing. (Stuffing is evil. Dressing is great.)
5) Check bird infrequently to keep heat in BBQ, Use thermometer and allow for 5 degree carryover. Let bird rest for 15-20 min. post BBQ.
This method works well because all poultry need the thighs to be cooked to a higher temp than the breast. The breast cover helps with that as does the fact that the heat from the two fires is directed up to the thighs to help them cook faster.
This method will deliver that crisp skin we love but shouldn't have. The brined bird will help keep the breast moist and the two side fires will cook the thighs faster as needed.
I've done this a few times in a 22" Weber kettle and the results were generally good. No real recipe, just salt the bird well before starting. Do not stuff, BTW.
I start out with enough coals to cover the grid less than 2 layers thick. That's before lighting. Start the coals and place in a ring on the outer part of the grid, center clear. You may put a pie pan in the middle to control the drips. Place the bird breast-up in the center of the grill, cover, and check back in maybe a half-hour and periodically after. When the coals seem to be exhausted put fresh ones in to replace them (you'll need somehwere tp out the grill with bird on top to get access, of course). Not too may coals in the beginning or on replacement. You don't want enough heat to burn things.
Sometime around when the second batch of coals is consumed start checking for doneness, either with a thermometer of the "jab with a fork and check the juice for color" method. Thermometer might be the better way, as you risk a slightly underdone bird with the clear-juice method (experience).
Seems to be somewhat faster than an oven and the whole bird is moist, no dry breast and red thigh. Maybe because the heat is held closely around the bird or because of no pan shielding the bottom of the bird. I've only done around 20 pounders, not sure if there's room for a bigger one.