In a large bowl, beat eggs lightly. Beat in condensed milk, evaporated milk and cream of coconut until smooth. Fold in grated coconut, vanilla and rum. Pour into a 9x13 inch baking dish.
Bake in preheated oven 1 hour, until pick inserted in center comes out clean. Turn oven off and let dish rest in oven 15 minutes. Remove from oven to cool completely. Chill before serving.
