Socially assistive robots are increasingly being explored to improve the engagement of older adults and people with disability in health and well-being-related exercises. However, even if people have various physical conditions, most prior work on social robot exercise coaching systems has utilized generic, predefined feedback. The deployment of these systems still remains a challenge. In this paper, we present our work of iteratively engaging therapists and post-stroke survivors to design, develop, and evaluate a social robot exercise coaching system for personalized rehabilitation. Through interviews with therapists, we designed how this system interacts with the user and then developed an interactive social robot exercise coaching system. This system integrates a neural network model with a rule-based model to automatically monitor and assess patients' rehabilitation exercises and can be tuned with individual patient's data to generate real-time, personalized corrective feedback for improvement. With the dataset of rehabilitation exercises from 15 post-stroke survivors, we demonstrated our system significantly improves its performance to assess patients' exercises while tuning with held-out patient's data. In addition, our real-world evaluation study showed that our system can adapt to new participants and achieved 0.81 average performance to assess their exercises, which is comparable to the experts' agreement level. We further discuss the potential benefits and limitations of our system in practice.