Qualifications
While most country club managers have a Bachelor's degree, what you need most is a degree in life experience. Country club managers need a wide range of experience and skills: sales and marketing, property maintenance, and community relations. You'll also need some knowledge of golf and gardening, too. What type of grass is best? How can you most economically maintain the grass? Lots of grass-related questions.
And, of course, experience in a country club setting is a major plus, as is any experience managing and operating restaurants and hotels.
If you can demonstrate your knowledge in those areas, no one's going to be asking you to produce some certification in Country Club Management (which doesn't exist, by the way).