1. Cook first 4 ingredients in a large saucepan over medium heat, stirring often, 30 minutes. Let cool slightly.
2. Sprinkle gelatin over 1/3 cup water in a small saucepan; let stand 1 minute. Cook over low heat, stirring until gelatin dissolves (about 2 minutes).
3. Process peach mixture in blender or food processor until smooth, stopping to scrape down sides. Stir in gelatin mixture and peach liqueur. Cover and chill 8 hours.