Preheat oven to 350 degrees, with rack in middle of oven. Butter an 8-by-11-inch tart pan and line bottom and sides with parchment paper.
Make the crust: Combine flour, coconut, sugar, and salt in a large bowl. Stir in melted butter and mix until dough is crumbly. Firmly press mixture into bottom of prepared pan. Bake until just golden, about 15 minutes. Remove and set aside to cool slightly.
Meanwhile, make the filling: Combine coconut, sugar, and egg whites. Stir until well combined.
Arrange blackberries in crust. Evenly top berries with small dollops of macaroon filling.
Bake for 20 to 25 minutes, until peaks of macaroon filling are deeply golden. Let cool, and garnish with pistachios. Slice into small squares.