Preheat oven to 350 degrees F (175 degrees C). Line 16 muffin cups with paper liners.
Beat sugar, olive oil, egg, and vanilla extract together in a bowl until light in color and creamy. Add bananas and coconut; stir to combine. Mix flour, baking soda, cinnamon, nutmeg, and salt into banana mixture until smooth. Spoon batter into prepared muffin cups.
Bake in the preheated oven until a toothpick inserted in the center of a cupcake comes out clean, 30 to 40 minutes.