In the bowl of a standing or electric mixer, cream butter and sugar until light and fluffy. Beat in lemon zest and extracts. Add flour and salt and beat well. Stir in coconut.
Cut dough in half and place each half on a sheet of waxed paper. Form each half into an 8-inch log. Wrap each log in waxed paper and refrigerate at least 4 hours (or overnight).
Adjust oven rack to middle position and heat to 300 degrees. Grease baking sheets or line with parchment paper. Cut logs into ¼-inch-thick slices with a sharp knife, and arrange 2 inches apart on prepared baking sheets. Bake 25 to 30 minutes, or until pale golden.
Transfer cookies to racks and sprinkle generously with confectioners’ sugar. Let cool and dust lightly with more confectioners’ sugar.