In a mixing bowl, combine juice of two limes, honey, oil, garlic, salt, pepper, paprika and 2 tablespoons cilantro. Whisk well and pour over chicken. Let marinate, refrigerated for about 8 hours of overnight.
Preheat an outdoor grill and add drumsticks. Discard any additional marinade. Cook for 15-20 minutes or until no longer pink and juice is clear. Sprinkle with remaining cilantro before serving.