Preheat the oven to 350 degrees F (180 degrees C). Line an 8-inch square baking dish with parchment paper, leaving some overhanging on all sides.
Arrange mango slices in an overlapping pattern over the bottom of the prepared dish.
Combine sugar, eggs, yogurt, and oil in a large bowl and stir until smooth. Fold in flour, coconut, and baking powder until just combined. Spoon batter over the sliced mango, and spread evenly to the edges.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 45 to 50 minutes. Let the cake cool in the dish for 15 minutes before inverting onto a serving plate and carefully peeling off the parchment paper. Allow to cool completely before slicing.