Preheat oven to 350°F (175°C). Grease a 9x9 inch baking dish.
In a mixing bowl, combine 1 cup flour and ¼ cup sugar. Stir in melted butter until mixture is crumbly. Press into the bottom of the prepared baking dish.
Bake crust for 15 minutes in the preheated oven. Remove and set aside.
In another bowl, whisk together 1 cup sugar and ¼ cup flour. Add eggs and lime juice, whisk until smooth. Stir in shredded coconut.
Pour filling over the baked crust. Bake for an additional 20-25 minutes, or until set. Let cool before cutting into bars.