In today's society, digital coaching systems for healthcare-related interventions are becoming increasingly prevalent. With the rise of intelligent healthcare systems, new opportunities have emerged for the design and development of solutions that are tailored to the specific needs and requirements of individual users. However, designing an intelligent system is challenging due to difficulties in specifying requirements, future users' expectations, and the system's adaptive behaviour during run-time. This paper focusses on the early phase design process of such systems for the use case of stress management. The methodology incorporates a combination of existing theory and model of stress management as well as two qualitative studies that elicit views of target users and experts. The outcome of this research includes design implications, expected behaviour, interactions and roles, and expected features and functionalities of an intelligent coaching system for stress management. The outcomes of this research lay the foundations to initiate design process of intelligent coaching systems. Finally, this research contributes to enriching understanding of initiating the design process of intelligent systems for digital wellbeing.