There is growing interest in psychological interventions using socially assistive robots to mitigate distress and pain in the pediatric population. This work seeks to address the deficit in understanding of what features and functionality young children and their parents desire to help with pain management by using co-design, a common approach to exploring participants' imaginations and gathering design requirements. To close this gap, we carried out a co-design workshop involving seven families (with children aged between 4-6 and their parents) to understand their expectations and design preferences for a robot designed for pain management in children. Data were collected from surveys, video and audio recordings, interviews, and field notes. We present the robot prototypes constructed during the workshops and derive several preferences of the children (e.g, zoomorphic shape, distractors and emotional expressions as behaviors). Additionally, we report methodological insights regarding the involvement of young children and their parents in the co-design process. Based on the findings of this co-design study, we discuss personalization as a possible design concept for future child-robot interaction development.