Preheat the oven to 350 degrees F.
Butter a 13 by 9-inch baking dish with 2 tablespoons of the butter.
In a large skillet, melt 2 tablespoons of the butter over medium heat. Add the pineapple and bananas and cook, stirring, until they begin to soften, about 5 minutes. Remove from the heat.
In a small saucepan, melt the remaining 2 tablespoons of butter.
In a large bowl, whisk the eggs. Add the cream, coconut milk, brown sugar, vanilla, cinnamon and allspice, and whisk well. Add the bread, fruit, and melted butter, and stir well to combine. Let sit until the bread is saturated. Pour into the prepared dish.
Bake until golden and firm when pressed in the center, about 1 hour. Remove from the oven and cool slightly on a wire rack to set, about 20 minutes.
Serve on dessert plates. Spoon the sauce over the pudding and sprinkle each serving with the coconut and confectioners' sugar.
Yield: 8 to 10 servings