With advancements in technology, the integration of social robots for real-world applications is increasing. There is an emerging need to conduct participatory research to ensure these technological interventions are effectively tailored to meet the specific needs and challenges of their intended users. Given the limited examples of robots in speech and language therapy, we employed a co-design approach involving active collaboration between human-robot interaction researchers and speech-language pathologists (SLPs). Over an 18-month period, the team engaged in a series of interviews, shadowing sessions, and regular co-design meetings. This process provided deeper insights into speech-language therapy for children in clinical settings and helped identify key design considerations for developing an approach integrated with a social robot. The resulting robotic system is tailored to meet the needs and preferences of SLPs, designed to seamlessly fit into existing speech therapy sessions in the clinic without disrupting the established therapy structure.