Preheat oven to 200°C/400°F/Gas Mark 5. On a lightly floured board, roll out pastry to ⅓ cm (1/8 in) thick and cut four 10 cm (4 in) rounds. Place these on a greased tray and leave to rest at room temperature for 20 minutes.
Mash two bananas with coconut and spread evenly over pastry. Slice remaining bananas on a slight angle, about ½ cm (¼ in) thick, and lay on top. Lightly brush pastry and banana with half the butter and sprinkle with sugar.
Bake in the middle of the oven until pastry is golden and bananas are lightly caramelised, about 15 minutes. Brush the remaining butter over the tarts and bake a further 2-3 minutes. Serve warm with runny cream or ice cream.