Does Confucius University in Beijing have a calligraphy major?

No. There is currently no Confucius University in Beijing. A Confucius Institute is a type of Confucius Institute located at a foreign university, rather than a higher education institution called a Confucius University. The Confucius Institute is a Chinese education institution established by Hanban (Confucius Institute Headquarters/Hanban) in cooperation with foreign universities.