The emergence of generative artificial intelligence (GenAI) has ignited discussions surrounding its potential to enhance creative pursuits. However, distinctions between children’s and adult’s creative needs exist, which is important when considering the possibility of GenAI for children’s creative usage. Building upon work in Human-Computer Interaction (HCI), fostering children’s computational thinking skills, this study explores interactions between children (aged 7-13) and GenAI tools through methods of participatory design. We seek to answer two questions: (1) How do children in co-design workshops perceive GenAI tools and their usage for creative works? and (2) How do children navigate the creative process while using GenAI tools? How might these interactions support their confidence in their ability to create? Our findings contribute a model that describes the potential contexts underpinning child-GenAI creative interactions and explores implications of this model for theories of creativity, design, and use of GenAI as a constructionist tool for creative self-efficacy.