For the marinade: Whisk together lime zest and juice, honey, oil, and minced garlic in a small bowl. Season drumsticks with salt, pepper and paprika and arrange in a glass container. Pour marinade over drumsticks, seal container and marinate in the refrigerator for 2-24 hours.
Heat an outdoor grill to medium.
Remove drumsticks from marinade, and discard marinade. Arrange drumsticks on grill over a medium flame and cook for 15 minutes, rotating every 3 minutes or until internal temperature reaches 165 degrees and juices run clear.
For the watermelon salad: In a large bowl, toss cubed watermelon with mint and crumbled feta. Serve cold, with chicken