See what Dr Scott Sicherer, from the magazine Allergic Living, has to say.

Q. I’ve read differing views on whether it would be safe for a nut-allergic person to eat baked goods with coconut or coconut oil. What’s your view on coconut?
 
Dr. Scott Sicherer: Despite its name, coconut is not actually a nut, but a fruit. Regardless, the Food and Drug Administration considers it a tree nut, which is why it’s included in U.S. labeling laws. 

It is difficult to assess the risk of coconut allergy among those with tree-nut allergies because allergic individuals may become wary of coconut and avoid it. Still, coconut allergy appears rare, and uncommon even among those with tree-nut allergies. To read the whole article please click here.