Preheat oven to 250 degrees F (120 degrees C). Grease a 9x13-inch baking dish.
Beat eggs in a large bowl until frothy. Add evaporated milk, coconut milk, sweetened condensed milk, rum, sugar, butter, raisins, vanilla extract, nutmeg, and cinnamon and mix well; fold in bread. Pour mixture into the prepared baking dish.
Bake in the preheated oven until browned and edges are beginning to look dry, about 1 hour.