The Australian tennis great who won all 10 of his Grand Slam doubles titles in the 1960s was Fred Stolle. The right-handed player became one of Australia’s outstanding doubles specialists during the amateur era and the beginning of the Open Era.
Stolle’s 10 Grand Slam men’s doubles championships came between 1962 and 1969. He won four titles with Bob Hewitt, four with Roy Emerson, and two with Ken Rosewall. His victories covered all four major tournaments, including Wimbledon, the Australian Championships, the French Championships, and the U.S. Championships.
His doubles record is sometimes overshadowed by his singles career. Stolle lost his first five Grand Slam singles finals, a remarkable sequence, before winning the 1965 French Championships and the 1966 U.S. Championships. He was also a seven-time Grand Slam mixed-doubles champion and represented Australia in three Davis Cup-winning teams, in 1964, 1965, and 1966.
Stolle turned professional in 1966, but his 10 Grand Slam doubles titles were all earned during the 1960s. That timing is the key distinction in the question.