Brush drumsticks with cooking oil. Sprinkle with salt and pepper.
In a covered grill, arrange preheated coals around a drip pan. Test for medium* heat above pan. Place the drumsticks on grill above the pan (not directly over coals).
Lower grill hood and grill for 45 minutes to 1 hour or until tender but no longer pink, turning once. Add coals to maintain heat as necessary. (For a gas grill, preheat grill. Reduce heat to medium. Adjust for indirect cooking. Place the turkey on grill rack, not directly over the heat. Grill as above.) Makes 4 servings.
To test for medium heat, you should be able to hold your hand over the heat at the height of the food for 4 seconds before you have to pull away.