Wearable technology has significantly improved the quality of life for older adults, and the emergence of on-body, movable robots presents new opportunities to further enhance well-being. Yet, the interaction design for these robots remains under-explored, particularly from the perspective of older adults. We present findings from a two-phase co-design process involving 13 older adults to uncover design principles for on-body robots for this population. We identify a rich spectrum of potential applications and characterize a design space to inform how on-body robots should be built for older adults. Our findings highlight the importance of considering factors like co-presence, embodiment, and multi-modal communication. Our work offers design insights to facilitate the integration of on-body robots into daily life and underscores the value of involving older adults in the co-design process to promote usability and acceptance of emerging wearable robotic technologies.