Preheat oven to 375 degrees F (190 degrees C). Line 6 muffin cups with paper liners.
Mash bananas and persimmon together in the bowl of a stand mixer. Add 3/4 cup sugar, coconut oil, egg, and vanilla extract, 1 at a time, mixing well after each addition.
Sift flour, baking powder, and salt together in a separate bowl. Stir flour mixture into banana mixture using a spoon just until batter is combined. Fill each muffin cup 3/4-full with batter.
Mix 1 tablespoon sugar and cinnamon together in a bowl; sprinkle over batter.
Bake in the preheated oven until a toothpick inserted in the center of a muffin comes out clean, 18 to 23 minutes.
