COMBINE rice, sweetened condensed milk, evaporated milk, Coffee-mate, vanilla extract, cinnamon and nutmeg in medium saucepan; whisk well. Cook over medium heat, stirring frequently, until almost boiling.
REDUCE heat to low; cook, stirring frequently, for 20 to 30 minutes or until thickened. Stir in coconut.
SERVE warm or chilled. If chilling, pour into serving bowls and cover with plastic wrap, making sure the wrap touches the surface of the pudding. Garnish with toasted coconut, if desired.