Mental health concerns are rising globally, prompting increased reliance on technology to address the demand-supply gap in mental health services. In particular, mental health chatbots are emerging as a promising solution, but these remain largely untested, raising concerns about safety and potential harms. In this paper, we dive into the literature to identify critical gaps in the design and implementation of mental health chatbots. We contribute an operational checklist to help guide the development and design of more trustworthy, safe, and user-friendly chatbots. The checklist serves as both a developmental framework and an auditing tool to ensure ethical and effective chatbot design. We discuss how this checklist is a step towards supporting more responsible design practices and supporting new standards for sociotechnically sound digital mental health tools.