Peel the fruit, cut it in half, remove the pit, and then cut it into pieces.
In a deep saucepan, combine the sugar and peaches, place it on the stove, and cook slowly until the sugar dissolves; then bring to a boil for 1 minute, then lower the heat.
Cook the fruit for 30 minutes over low to medium-low heat, stirring occasionally. If the fruit releases a lot of liquid during cooking, extend the cooking time by 10–15 minutes.
When the fruit is almost done cooking, soak the gelatin sheets in a little cold water for 10 minutes. Then squeeze out the excess water and melt the gelatin on the stove using a few spoonfuls of the fruit mixture.
When the pudding is lukewarm, add the melted gelatin, stir vigorously, and pour into a pudding mold lined with plastic wrap.
Store in the refrigerator overnight before serving.