Health coaching helps patients identify and accomplish lifestyle-related goals, effectively improving the control of chronic diseases and mitigating mental health conditions. However, health coaching is cost-prohibitive due to its highly personalized and labor-intensive nature. In this paper, we propose to build a dialogue system that converses with the patients, helps them create and accomplish specific goals, and can address their emotions with empathy. However, building such a system is challenging since real-world health coaching datasets are limited and empathy is subtle. Thus, we propose a modularized health coaching dialogue with simplified NLU and NLG frameworks combined with mechanism-conditioned empathetic response generation. Through automatic and human evaluation, we show that our system generates more empathetic, fluent, and coherent responses and outperforms the state-of-the-art in NLU tasks while requiring less annotation. We view our approach as a key step towards building automated and more accessible health coaching systems.