The last decade has shown a growing interest in robots as well-being coaches. However, cohesive and comprehensive guidelines for the design of robots as coaches to promote mental well-being have not yet been proposed. This paper details design and ethical recommendations based on a qualitative meta-analysis drawing on a grounded theory approach, which was conducted with three distinct user-centered design studies involving robotic well-being coaches, namely: (1) a participatory design study conducted with 11 participants consisting of both prospective users who had participated in a Brief Solution-Focused Practice study with a human coach, as well as coaches of different disciplines, (2) semi-structured individual interview data gathered from 20 participants attending a Positive Psychology intervention study with the robotic well-being coach Pepper, and (3) a participatory design study conducted with 3 participants of the Positive Psychology study as well as 2 relevant well-being coaches. After conducting a thematic analysis and a qualitative meta-analysis, we collated the data gathered into convergent and divergent themes, and we distilled from those results a set of design guidelines and ethical considerations. Our findings can inform researchers and roboticists on the key aspects to take into account when designing robotic mental well-being coaches.