Preheat oven to 325F.

Place the sugar in a small, uncoated skillet. Heat the sugar over medium-high heat until melted and golden brown. Pour it into a 1-quart baking dish or distribute evenly among eight 1-cup capacity ramekins. Tip and turn the dish or ramekins to coat the bottom and sides with the melted sugar.

Whisk the eggs in a large bowl until foamy. Stir in the condensed milk, cream of coconut, half-and-half, vanilla, and rum. Pour the mixture into the baking dish. Put the baking dish in a larger baking an and set it in the oven. Pour enough boiling water into the larger pan to reach halfway up the sides of the baking dish or ramekins.

Bake 1 hour for the 1-quart or 45 minutes for the ramekins, until the center is almost set. Remove the flan from the pan of water and cool on a rack. Invert onto a serving plate; cover and refrigerate at least 1 hour before serving*. The flan will keep for up to 3 days in the refrigerator.