A hot course at Harvard Business School promises to teach future leaders an elusive skill—managing happiness. One of the toughest parts is just getting a spot in the class.

As business schools train the corporate chieftains of tomorrow, skills like emotional awareness and improving well-being are taking their places alongside deal making and financial modeling. Courses on happiness, relationships and balance are among the most in-demand courses at top M.B.A. programs. Their popularity reflects both the demand for soft skills and students’ desire for more-balanced lives—and an intention among schools to turn out better bosses.