Preheat oven to 350°F.
In a medium bowl or the bowl of a food processor, combine the butter, sugar, flour and salt, blending with a pastry cutter or fork or pulsing in the food processor until well-combined and crumbly. Press into the bottom of a buttered or parchment-lined 8x8-inch pan and bake for 8-10 minutes, or until pale golden around the edges.
In the same bowl, combine the sugar, flour, baking powder and salt. Add the eggs, lemon zest and lemon juice and stir until well blended and smooth.
Sprinkle the cranberries and coconut evenly over the base and pour the lemon filling over top. Bake for 30-35 minutes, or until golden and set. Cool completely in the pan on a wire rack before cutting into squares; freeze them first for a cleaner cut. Once cooled, sprinkle with icing sugar before serving. (If you want to cut them really cleanly, cool and freeze, then cut them frozen.)
Makes 16 squares.