This Late-Breaking Work explores the significance of socio-emotional learning (SEL) and the challenges inherent in designing child-appropriate technologies, namely storytelling agents, to support SEL. We aim to probe their needs and preferences regarding agents for SEL by conducting co-design which involves children co-creating characters and social-emotional stories. We conducted collaborative story-making activities with children aged four to six years old. Our findings could inform the design of both verbal and nonverbal interactions of agents, which are to be aligned with children's understanding and interest. Based on the child-led peer co-design, our work enhances the understanding of SEL agent designs and behaviors tailored to children's socio-emotional needs, thereby offering practical implications for more effective SEL tools in future HCI research and practice.