Artificial intelligence (AI) is increasingly framed as a collaborative partner in creative activities, yet children's interactions with AI have largely been studied in AI-led instructional settings rather than co-creative collaboration. This leaves open questions about how children can meaningfully engage with AI through iterative co-creation. We present Tinker Tales, a tangible storytelling system designed with narrative and social-emotional scaffolding to support child-AI collaboration. The system combines a physical storytelling board, NFC-embedded toys representing story elements (e.g., characters, places, items, and emotions), and a mobile app that mediates child-AI interaction. Children shape and refine stories by placing and moving story elements and interacting with the AI through tangible and voice-based interaction. We conducted an exploratory user study with 10 children to examine how they interacted with Tinker Tales. Our findings show that children treated the AI as an attentive, responsive collaborator, while scaffolding supported coherent narrative refinement without diminishing children's agency.