Combine sugar, 2 cups water, and 2 1/2 tablespoons lime juice in a medium saucepan; bring to a boil. Reduce heat, and simmer for 5 minutes or until sugar dissolves. Remove from heat. Place the sugar mixture in an airtight container, and chill.
Stir in remaining 1/4 cup lime juice, pineapple juice, and rind. Pour mixture into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions, adding fresh pineapple during the last 10 minutes.