Preheat the oven to 325 degrees . In a small, heavy saucepan, cook the sugar over medium heat, stirring constantly, for about 3 minutes, until it has dissolved and turned caramel color. Quickly pour the caramel into a 10-inch deep-dish pie plate and carefully turn the pie plate to swirl the caramel over the bottom and around the sides of the plate.
In a large bowl, beat the eggs well, then whisk in the evaporated milk, sweetened condensed milk, cream of coconut and vanilla until combined. Pour the mixture into the prepared pie plate and place the pie plate inside a large roasting pan with handles. Place the roasting pan in the oven and add warm water to the pan until it is about 1 inch deep. Bake the flan until it is set but still slightly jiggly in the center, about 1 hour.
Remove the roasting pan from the oven. Carefully remove the pie plate from the roasting pan and let the flan cool on a wire rack, then refrigerate for 4 hours or overnight. To serve, run a small spatula around the edge of the pie plate. Place a serving plate over the pie plate and invert to release the flan; cut into wedges to serve.