Coconut oil is safe to use under your eyes but just be careful to not get any coconut oil in your eyes.
You can use coconut oil under your eyes to help moisturize your eyelids and help prevent fine lines and wrinkles under your eyes.
You can also reduce the appearance of under eye bags by massaging some coconut oil under your eyelids.
Coconut oil can also help get rid of dark circles under your eyes as well and use of the coconut oil daily can help keep your skin moisturized and get rid of the wrinkles and tighten the skin.
You can also buy special made coconut oil eye drops to help reduce dry eyes but don't put coconut oil directly into your eyes.
But just use the coconut oil under your eyes and it will be safe.