Preheat oven to 350 degrees F (175 degrees C). Grease a cookie sheet.
In a bowl, thoroughly mix the brown sugar, oats, butter, coconut, all-purpose flour, self-rising flour, pineapple, egg, lime juice, lime zest, and vanilla extract.
Drop by rounded spoonfuls onto the prepared cookie sheet.
Bake 12 to 15 minutes in the preheated oven, until lightly browned. Cool on wire racks.