Move oven rack to upper-most level and pre-heat oven to 425 degrees F. In a small bowl, mix coconut oil and herbs until well distributed. Remove excess moisture from the drumsticks, one at a time, by wrapping with a paper towel and gently squeezing. Use your fingers to create space between the meat and the skin.
Place a small amount of the oil/herb mixture under the skin and over the skin, making sure that some of the herbs stick to the drumstick. Place drumsticks in a roasting pan, sprinkle with salt, and bake, uncovered, for 45 minutes.
Increase oven temperature to 500 degrees F and cook for an additional 10 minutes, until skin is crispy and meat registers at 165 degrees F.