Whether you choose chicken, duck, turkey or game hen, marinate your poultry or try a dry rub ahead of time to maximize flavor. Once you've selected your specific poultry and seasoning method, prep the grill and cook accordingly:
Thin pieces of poultry can be cooked over direct heat; larger pieces of chicken should be cooked over indirect heat. Cook bone-in breast and leg/thigh pieces for 12-15 minutes per side, wings 2-3 minutes per side; boneless breasts 4-6 minutes per side. Turning the pieces every 2-5 minutes and rotating pieces around the grill can help ensure even cooking.
Cook whole chickens breast-side down using the indirect method, place a drip pan under the chicken and cook with the lid closed. Open the bottom vents and close the top vents of the grill halfway. Cook for 20 minutes, turn, baste and cook for 15–20 minutes per pound. A 3 to 4 pound chicken will cook in approximately 1¾ hours.
To cook a turkey breast, first make sure it fits your grill (ideally leave a minimum of one inch clearance from the lid). Use the indirect cooking method, setting a drip pan below the turkey, and cook with the lid closed. Depending on the bird's weight, grill a smaller boneless breast (up to 3 pounds) about 1 to 1½ hours. A larger boneless breast (3 to 9 pounds) should take about 2 to 3 hours. Allow the turkey to rest 20 minutes before carving. Remember that smoked turkey may appear a little pink even when thoroughly cooked. (Cook stuffing in the oven, not with the breast.)
Always cook poultry thoroughly. Test for doneness with an instant read thermometer (it should reach 165°F). Insert the thermometer into the middle of the thickest part of the meat, taking care not to touch bone. Wait a couple of minutes before reading. For whole poultry, insert the thermometer into the thickest part of the thigh.
Chicken that is cooked enough will feel springy when pressed. If you're uncertain, cut into the thickest part of one piece. The meat should still be juicy, but the juices should be clear, never reddish.