Quarter the apples and plums, but leave their skins on; core the apples and remove the plum pits. Place the fruit in a 6-to-10-cup rice cooker. Add the apple juice, sugar, cinnamon sticks and butter. Cover and cook on the porridge cycle, or program for 50 minutes.
Discard the cinnamon sticks. Stir and mash the fruit with a potato masher to make a chunky sauce. Serve warm or at room temperature.