Chances are, even if you can't eat some (or all) nuts, you will probably be fine with coconut. The proteins (which are the allergens) are very different and coconut allergy is rare.
Source: The Australasian Society of Clinical Immunology and Allergy http://www.allergy.org.au/content/view/171/1/
fungi like aspergillus Niger and mucor
1/2 of a coconut is approx 3/4 cup
making 1 coconut approx 1.5 cups or approx 12-14 ounces
There are 1 1/3 cups of coconut in a small can. Ada