Preheat oven to 350°F Line bottom and sides of a 13 x 9-inch pan with heavy-duty aluminum foil, allowing 2 inches to extend over sides; lightly grease foil.
Stir together 1 3/4 cups flour and 1/2 cup sugar. Cut in butter with a pastry blender or fork until crumbly. Press mixture onto bottom of prepared pan.
Bake at 350F for 20 to 23 minutes or until lightly browned.
Meanwhile, whisk eggs in a medium bowl until smooth; whisk in coconut, lime zest and juice and tequila and remaining 1 1/2 cups sugar. Stir together baking powder, salt and remaining 1/4 cup flour; whisk into egg mixture. Pour over hot crust.
Bake at 350F for 25 minutes or until filling is set. Let cool 1 hour on a wire rack. Lift from pan, using foil sides as handles,.