Göncz was a senior officer at Magyar Posta before turning professional as a tennis player and coach. He participated in the 1924 Summer Olympics, where he was defeated by René Lacoste in men's singles at the second round (0–6, 0–6, 1–6). He also played in men's doubles, alongside Kálmán Kirchmayr, where they defeated by R. Norris Williams and Watson Washburn (1–6, 0–6, 0–6). Following his player career, Göncz became a coach and lecturer at the Hungarian Royal College of Physical Education. In early 1930s, he was head coach of Hungary's tennis youth team within the Hungarian Tennis Association.