Preheat the oven to 350 degrees F (175 degrees C).
Mix 1/3 cup coconut, brown sugar, rum, melted butter, and 1/4 of the pineapple juice together in a bowl. Pour into the bottom of a 2 1/2-quart casserole dish. Place bread cubes on top.
Mix coconut milk beverage, orange juice, white sugar, eggs, remaining coconut, remaining pineapple juice, cinnamon, and nutmeg together in large bowl. Pour over bread cubes and sprinkle with a little cinnamon.
Bake in the preheated oven until a knife inserted in the center comes out clean, 50 to 60 minutes.