This paper focuses on establishing best practices for artificial intelligence (AI) design for children. To propose a design grammar that meets the developmental needs of children, we combine Piaget's theory of cognitive development with an analysis of 52 animated films to present six design-based frameworks applicable to child-centered AI design. This framework includes cues for visual vividness and clarity, sound for musical and auditory scaffolding, audiovisual cues for synchronization, facilitator-style personas, storyplay to support symbolic play and imaginative exploration, and predictable narrative structures. These strategies, long refined in animation, serve as multimodal scaffolds that support children's learning and comfort. This structured design grammar can be applied to AI design, and by reconstructing cinematic storytelling and child development theory into AI design logic, we provide heuristics for AI design that cater to the cognitive and emotional needs of young users.