Combine 2 cups coconut and evaporated milk in a medium saucepan over medium heat, and cook until tiny bubbles form around edge (do not boil), about 7 minutes.
Remove from heat. Cover and chill at least 4 hours or up to overnight.
Arrange pineapple in a single layer on a baking sheet; freeze at least 1 hour or until firm.
Strain coconut mixture through a sieve over a medium bowl, pressing coconut with the back of a spoon to remove as much milk as possible. Discard solids.
Combine pineapple, ice cubes, rum, juice, and agave nectar in a blender; process mixture until smooth.
