1. Drain mango slices, reserving 1/2 cup liquid. Process mango slices and peaches in a blender until smooth, stopping to scrape down sides. Pour peach mixture into a large container.
2. Process reserved mango liquid, cream of coconut, and lemonade concentrate in blender until smooth. Add coconut mixture and rum to peach mixture, stirring until combined. Use immediately.
3. Process 3 cups peach mixture with 2 cups ice in a blender until smooth. Repeat with remaining peach mixture and ice.
*1 (20-oz.) bag frozen sliced peaches, thawed, may be substituted.