Preheat the oven to 350°F. Grease a 9 x 5-inch loaf pan with cooking spray and lightly flour the pan; set aside.
Lightly spoon the 1 cup all-purpose flour and 1 cup whole wheat flour into dry measuring cups, level with a knife, and add both flours to a large bowl.
Add 3/4 teaspoon baking soda and 1/2 teaspoon salt to the flour mixture and whisk to combine; set aside.
In a separate mixing bowl, place 1 cup sugar and 1/4 cup coconut oil. Beat with an electric mixer at medium speed until well blended.
Add the 2 large eggs to the sugar mixture one at a time, beating well after each addition.
Peel and thoroughly mash the 3 medium bananas with a fork. Add the mashed bananas, 1/4 cup plain low-fat yogurt, 1 tablespoon lime juice, and 1/2 teaspoon vanilla extract to the mixing bowl and beat until combined.
Add the flour mixture to the wet mixture and beat at low speed just until the dry ingredients are moistened. Do not overmix.
Measure out the 3/4 cup coconut flakes: fold 1/2 cup coconut flakes into the batter, and reserve the remaining 1/4 cup for the topping.
Spoon the batter into the prepared loaf pan and evenly sprinkle the reserved 1/4 cup coconut flakes on top. Gently press the coconut into the batter with the back of a spoon to adhere (do not mix).
Bake at 350°F for 45 to 60 minutes. Begin checking at 45 minutes. The bread is done when a toothpick inserted into the center comes out clean or with a few moist crumbs.
Remove the pan from the oven and let the loaf cool in the pan for 10 minutes. Then transfer the loaf to a wire rack to finish cooling before slicing.