Preheat oven to 400 degrees F.
Place sliced bananas in a medium bowl and stir in crushed pineapple with juice. Toss gently until slices are coated. Allow to soak for 30 minutes, then drain. Place banana mixture in an unbaked pie shell.
In a small bowl, mix sugar and cinnamon. Reserving 2 tablespoons, sift over the top of the bananas. Dot with slices of butter and place the top crust on and seal. Make 2 to 3 vents near the center and brush with egg white or heavy cream, sprinkle with the 2 tablespoons of cinnamon sugar and flaked coconut.
Bake in preheated oven until the crust is golden brown, about 45-55 minutes. Pie can be served hot or cold.