I've actually been told that coconut oil isn't suitable for the face.
Castor oil is meant to be good - someone here recently tried it under the eyes and found it got rid of her dark circles.
"I think the basic anti-aging diet is also the best diet for prevention and treatment of diabetes, scleroderma, and the various "connective tissue diseases." This would emphasize high protein, low unsaturated fats, low iron, and high antioxidant consumption, with a moderate or low starch consumption.
In practice, this means that a major part of the diet should be milk, cheese, eggs, shellfish, fruits and coconut oil, with vitamin E and salt as the safest supplements."
- Ray Peat