Preheat the 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 it evenly among eight 1-cup capacity ramekins (about 2 tablespoons per ramekin). Tip and turn the dish or ramekins to coat the bottom(s) 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 large baking pan 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(s) 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(s) will keep for 3 days in the refrigerator.