Place eight 5-ounce paper cups in a shallow baking pan. In a medium bowl, combine pineapple and vodka; let stand at room temperature for 1 hour, stirring occasionally. Transfer to a blender container; add pineapple juice and pepper, if desired. Cover and blend until smooth. Add banana; pulse with on/off turns until chopped.
Pour into paper cups. Cover each cup with a square of foil. Use a small knife to make a small hole in center of each foil square. Slide a wooden craft stick or straw through each hole and into the mixture in the cup. Freeze overnight.
To serve: Peel paper cup off the pop. Serve at once or place in a larger glass set in ice.