Peel shrimp, leaving tails intact. Devein, if needed. Rinse well and drain thoroughly.
Pour oil to depth of 1-inch/2.5-cm into a Dutch oven or deep fryer; heat to 350F/180C.
Combine baking mix and beer in a small bowl; stir until smooth. Mixture should resemble pancake batter.
Dredge shrimp in flour; shake off excess. Dip shrimp into batter; dredge in coconut. Fry, a few at a time, 45 seconds on each side or until golden. Drain on paper towels.