Place an 8x1-1/2-inch round baking pan in oven. Heat oven to 200°F.
For caramel, in a heavy small saucepan combine sugar and the water. Cook over medium heat, without stirring, about 13 minutes or until amber-colored.
Using oven mitts, remove baking pan from oven. Carefully pour sugar mixture into baking pan, turning pan until bottom and sides of pan are coated. Let stand on a wire rack until cool. Lightly butter any uncoated spots on pan.
Increase oven temperature to 350°F. In a small saucepan combine half-and-half and cream of coconut. Bring to boiling, stirring occasionally.
In a medium bowl whisk together eggs and egg yolks. Slowly whisk coconut cream mixture into egg mixture; add rum, vanilla, and allspice.
Place coated baking pan in a small roasting pan. Pour egg mixture into coated pan. Place on middle rack in oven. Pour enough boiling water into roasting pan to come halfway up baking pan.
Bake for 35 to 45 minutes or just until knife inserted near center comes out clean. Let cool in pan on a wire rack. Chill for 2 to 6 hours.
To serve, run a knife around edge of baking pan. Invert serving platter on top of baking pan; carefully turn platter and pan over together, letting caramel run over top and side of flan. Remove baking pan. Sprinkle flan with toasted coconut.