Preheat the oven to 350 degrees. Toss the coconut with the salt on a rimmed baking sheet. Toast this in the oven, stirring frequently until golden brown, which should take 8 to 10 minutes. Once the mixture is cool, crush it with your hands until it is crumbly.
Pour 2 tablespoons of lime juice into a shallow dish. Dip the rims of the cocktail glasses in lime juice, then into coconut mixture, coating it well.
Combine the remaining ingredients with 1 cup ice in a blender and puree until the mixture is smooth. Pour evenly in prepared glasses and serve immediately.