Preheat the oven to 350 degrees F (175 degrees C). Lightly spray a 12-cavity doughnut pan with cooking spray.

Combine sugar and eggs in a large bowl; beat with an electric mixer until smooth and creamy. Add bananas, yogurt, oil, and vanilla extract; mix until incorporated. Add whole wheat flour, all-purpose flour, cinnamon, baking soda, baking powder, and salt; mix until combined. Transfer batter to a resealable plastic bag.

Snip off one corner of the bag and pipe batter into the prepared doughnut pan.

Bake doughnuts in the preheated oven until slightly browned on the bottoms, 10 to 12 minutes. Remove from pan and transfer to a wire rack to cool completely.