Children with autism spectrum disorder (ASD) experience challenges in grasping social-emotional cues, which can result in difficulties in recognizing emotions and understanding and responding to social interactions. Social-emotional intervention is an effective method to improve emotional understanding and facial expression recognition among individuals with ASD. Existing work emphasizes the importance of personalizing interventions to meet individual needs and motivate engagement for optimal outcomes in daily settings. We design a social-emotional game for ASD children, which generates personalized stories by leveraging the current advancement of artificial intelligence. Via a co-design process with five domain experts, this work offers several design insights into developing future AI-enabled gamified systems for families with autistic children. We also propose a fine-tuned AI model and a dataset of social stories for different basic emotions.