In a medium bowl, stir together 1 1/4 cups flour, baking powder, salt, and coconut. In a large bowl with an electric mixer, beat the butter and sugar until smooth and creamy, 2 to 3 minutes. Beat in the egg and zest.
Beat the flour mixture into the butter mixture in 2 additions until completely mixed, about 1 minute. Turn the dough out onto a work surface floured with 1 tablespoon flour and gently knead just until the flour is absorbed and a smooth, soft but not sticky dough forms. Wrap in plastic wrap and refrigerate until firm, at least 20 minutes.
Lightly butter 8 individual 3-by-1-inch (7 1/2 cm) round tartlet tins and place them on a rimmed baking sheet.
Divide the dough into 8 equal portions and roll each portion into rounds more than 1/8-inch (1/4 cm) thick. Line the tartlet tins, carefully lifting the dough, pressing it into place, and pinching together any tears in the soft dough. Trim any excess dough above the edges. Refrigerate the tartlet shells while the oven preheats.
Preheat the oven to 400°F (200°C).
Line each shell with parchment or foil, fill with pastry weights or dried beans, and bake for 6 minutes. Carefully lift out the weights and parchment, and return the shells to the oven, uncovered, until golden brown, 8 to 12 minutes. Let cool completely on wire racks.