This paper explores the design challenges that arise in supporting online freelancers to navigate relationships with clients. Prior studies have shown that current platform designs can lead to worker precarity in freelancer-client relationships, such as power imbalances, information asymmetry, and labor abuse. To envision alternative designs that empower workers in managing their relationships with clients, we engaged 22 Upwork freelancers in participatory speculative design activities. Through this co-design process, we identified design tensions that constrain design options as a result of conflicting values and priorities that could only be balanced and compromised rather than completely resolved. Six design tensions were identified in the context of designing for four different phases of freelancing. We observed three patterns in these tensions: 1) the freelancers' need for client involvement in their tasks and career growth, which conflicted with their skepticism that clients had sufficient incentives to be involved; 2) that there was often no viable balancing option for some tensions, but they could be addressed through changes in the platform's incentive structure; and 3) some tensions occurred not only between freelancers and clients, but also within the freelancer community. We present three approaches for addressing these design tensions and discuss how this research can support more equitable and healthy freelancer-client relationships.