Global sustainability challenges depend on large-scale behavioral change. Persuasive conversational agents (CAs) have emerged as promising systems to shape user attitudes and foster sustainable actions. However, the design knowledge surrounding these systems is scattered and seldom reused. This paper follows a metasynthesis approach and consolidates insights from 26 publications directly addressing persuasive CAs and sustainability. We extracted and clustered over 500 design knowledge chunks into 30 abstract design clusters, which are organized in a three-dimensional framework: Sustainability by agent (how CAs foster sustainability goals), sustainability in agent (how CAs embed ethical and inclusive practices), and conversational agent (core CA features for naturalistic interaction and adaptability). Our findings illuminate current design practices, uncover blind spots, and lay the groundwork for advanced theorizing. This structured resource enables researchers and practitioners to systematically identify important chunks to design, implement, and evaluate persuasive CAs that reinforce sustainable behaviors while maintaining responsible practices. By synthesizing fragmented insights into a reusable knowledge base, we promote consistency in future design efforts and offer a firm foundation for developing an overarching design theory of CA-based interventions for sustainability.