This paper presents a comprehensive review of fifty-two studies co-designing conversational agents (CAs). Its objectives are to synthesise prior CA co-design efforts and provide actionable recommendations for future endeavours in CA co-design. The review systematically evaluates studies' methodological and contextual aspects, revealing trends and limitations. These insights converge into practical recommendations for co-designing CAs, including (1) selecting the most suitable design technique aligned with desired CA outcomes, (2) advocating continuous stakeholder involvement throughout the design process, and (3) emphasising the elicitation and embodiment of stakeholder values to ensure CA designs align with their perspectives. This paper contributes to standardising and enhancing co-design practices, promising to improve the quality of outcomes in the case of CAs while benefiting stakeholders and users.