This paper presents the results of research aimed at developing a methodology for the participatory design of social robots, which are meant to be incorporated into various social contexts (e.g. home, work) and establish social relations with people. In contrast to the dominant technologically driven robot development process, we aim to develop a socially robust and responsible approach to robot design using Participatory Design (PD) methods. The PD process builds on participants' self-identified issues and concerns, and develops robot concepts according to participants' interpretations of the capabilities and potential applications of robotic technologies. We present methodological insights from an ongoing PD project aimed at designing socially assistive robots with older adults diagnosed with depression and their therapists, and identify remaining challenges in this project. We particularly focus on supporting mutual learning between researchers and participants and on promoting active participation of older adults as "designers" (rather than consumers) as foundational aspects of PD. We conclude with reflections regarding how this work can contribute to the further development of social robots and relevant PD methodologies.