Social robots have been utilized in education, healthcare, customer service, and domestic environments. However, there is limited research on their role in promoting sustainable living at home through playful interactions. This study extends the theme of family-robot interaction (FRI) within human-robot interaction (HRI) by integrating social robots and game-based interactions to enhance sustainability at home. We conducted a one-month qualitative study with 32 participants (parents and children) from eight families, using a family-centered design approach and participatory co-design method. Each family hosted a robot at home for one month. Through co-design sessions, they first shared their expectations for how social robots could support eco-friendly living, then ideated robot-based games to promote sustainability. Our findings showed that social robots were perceived as more engaging and appealing to children than adults. Children saw social robots as companions and were eager to learn pro-environmental practices through the robots’ interactive and playful features. The study’s eco-friendly focus, along with the co-design tasks around the robot, inspired some children to participate in sustainable living practices at home and encouraged their parents to do the same. The ideated robot-based games incorporated competition, collaboration, and reward elements, aiming to enhance interest and eco-friendly living and awareness. Overall, adults were more reserved about social robots, expressing concerns about the robots’ ability to maintain long-term engagement once the novelty effect fades. This study suggests that social robots have the potential to raise intergenerational environmental awareness at home, with children acting as the primary interest group who transfer their eco-friendly knowledge to their parents.