In a medium bowl, stir together 1 1/4 cup flour and 1/3 cup brown sugar. Rub in 1/2 cup butter using your hands or a pastry blender. Press into an ungreased 9 inch square pan.
Bake for 15 minutes in the preheated oven, or until lightly browned at the edges. Set aside. In a medium bowl, beat eggs until light. Mix together the brown sugar, flour, baking powder, and salt; stir into the eggs. Mix in the coconut, nuts, and cherries; spread the batter evenly over the baked crust.
Return to the oven, and bake for 25 minutes, or until brown. Set aside to cool. In a small bowl, mix the confectioners' sugar, 2 tablespoons butter, vanilla, and water until smooth. Add more liquid if necessary to make a more spreadable mixture. Spread over cooled bars before cutting into squares.
