Preheat oven to 350˚F.
In a large bowl, whip eggs, and add cream of coconut, half-and-half, and milk. Mix well. Add sugar and pineapple, and mix well. Grease a 9 x 13-inch pan. Break hamburger buns into pieces and place in pan. Sprinkle toasted coconut evenly throughout the bun pieces. Pour mixture over buns. Using your fingers, make sure that all bun pieces are soaked with the mixture.
Bake for approximately 45 minutes.

Rum Sauce

In a small saucepan, simmer cream of coconut and pineapple juice on medium heat.
Add sugar and cook for 3 more minutes. Add half-and-half and rum and cook for 5 more minutes or until slightly thickened.
Serve over warm bread pudding.