Caribbean and Bahamas Rum Punch Recipe Rum Punch | Credit By Islands Staff June 1, 2011 SERVES 1 1 1/2 oz. dark rum 1/4 oz. lime juice 2 oz. orange juice 2 oz. pineapple juice Dash of bitters 1. In a tall glass add ingredients to ice. Add grenadine for color and sprinkle with nutmeg.