Process the Nilla Wafers and 1 cup of the powdered sugar in a food processor until finely ground, 1 to 2 minutes. Add lime zest, lime juice, and corn syrup, and pulse until mixture just begins to come together, 2 to 3 times. Add coconut, and pulse until mixture comes together completely.
Shape dough into about 30 (1-inch) balls. Place remaining ⅓ cup powdered sugar in a shallow bowl; roll each ball in powdered sugar until coated. Serve immediately, or store in an airtight container at room temperature for 4 to 5 days.