Mix together powdered sugar and water on a small saucer until smooth. Spread coconut in a shallow layer on another saucer. Dip the rum of a martini glass in the sugar mixture until the rum is coated. Then, dip the sugared rim into the coconut. Use a spoon to pack the coconut on to the sugar coating so it stays on the rim.
Add the cranberry juice, coconut rum, and grenadine into a cocktail shaker with ice. Shake and strain into a prepared Martini glass and serve. Garnish with a candy cane.