Add chopped bread and pineapples to a bowl. Preheat the oven to 350°F (175°C). Grease a 9x13-inch baking dish with butter or cooking spray.
In a large mixing bowl, whisk the coconut milk, coconut rum, eggs, sugar, vanilla extract, molasses, cinnamon, and salt until well combined.
Add the cubed bread to the bowl and gently toss until all the cubes are coated in the coconut milk mixture. Let it sit for 10 minutes, allowing the bread to soak up the liquid.
After soaking, gently fold the diced mango and shred the coconut until evenly distributed throughout the bread mixture.
Pour the bread pudding mixture into the prepared baking dish, spreading it out evenly.
Bake in the oven for 40-45 minutes or until the pudding is set and golden brown on top.
Once baked, remove it from the oven and let it cool slightly before serving.