Coconut oil can be applied around your eyes safely but you should avoid getting coconut oil directly into your eyes.
If you do happen to get some coconut oil in your eyes accidentally then you really should wash it out immediately to avoid irritation of your eyes.
The coconut oil could cause your eyes to sting and burn and could potentially cause blindness if you do not remove the coconut oil.
When applying coconut oil to your eyes you should apply a little bit at a time and use a mirror in front of you to see where you're applying the coconut oil.
I once got some coconut oil in my eyes accidentally and it started burning after a few hours so I had to wash it out.
Now whenever I used coconut oil on my eyes I used a mirror to see where I'm actually putting it and so far I haven't gotten anymore coconut oil in my eyes.