Grease a 14cm x 21cm loaf pan, line the base with paper, then grease again. Beat the butter and sugar in a small bowl with an electric mixer until fluffy and pale in colour. Add the eggs one at a time, beating well after each addition. Stir in the coconut, sifted flours, sour cream and bananas, then mix well. Spoon the mixture into the prepared pan.
Cook in a slow/moderate oven (325°F) for about 50 minutes, or until cooked when tested with a skewer. Stand for 5 minutes before turning onto a wire rack to cool. Ice with a soft lemon whipped icing (beat together softened butter, icing sugar, warm lemon juice).