Born in Hungary, he took up football after emigrating to Australia at age 10 in 1957. Attila played his senior debut for Melbourne Hungaria in 1962 at 15 years of age in the old Victorian State League. In 1967 Abonyi was a key player in helping the club achieve their first ever State League title. He was the top goalscorer for that season with 31 goals in 29 games, and he scored the goal that won them the title. In that same year Abonyi was man of the match in helping Melbourne Hungaria win the Australian Cup, with a hat-trick, to defeat the favoured APIA Leichhardt 4-3 in extra-time. This turned out to be his final season with Melbourne Hungaria. He moved to Sydney and joined St. George-Budapest between 1969 and 1976 where he was part of three NSW State League titles, before finishing his career with Sydney Croatia between 1977 and 1979. In June 1975, Abonyi made a guest appearance for a touring Manchester United side, coming on as a substitute for David McCreery against Queensland. He scored United's third goal in a 3–0 win.
International career
Abonyi made his debut for Australia in November 1967 when the national team traveled to Vietnam for a friendship tournament. He scored a hat-trick on debut against New Zealand, and then scored another hat-trick in his second match against Singapore a few days later. He is well known for being a member of the Australian 1974 World Cup squad in West Germany and also represented New South Wales and Victoria. He scored 25 international goals for Australia in 61 games between 1967 and 1977 making him tied as the third highest goal scorer for Australia. He made a total of 88 appearances for Australia and scored 36 goals.
Managerial career
After retiring in 1979 Abonyi switched to coaching at the state level after taking on the player-coach for the 1978 and 1979 seasons. Sydney Croatia won the minor premierships in those two years. Abonyi then moved to Melita as a coach only, where they won the minor premiership and lost the grand final. He was then offered a full-time job with Riverwood, the only full-time coaching position in the state league at the time. In his first season they finished seventh and then runners-up in 1982 on goal difference to Sydney Croatia. He moved to Canberra in 1983 and coached Canberra City in the National Soccer League. For the 1984 season Sydney Croatia in their first season in the NSL offered Abonyi the head coach position, which he accepted. He was sacked halfway through the season because of poor results and high expectations by the board. In 1987 and 1988 and assisted Frank Arok at St. George who were in the NSL. After the 1988 season, Abonyi moved away from Sydney and football.
Honours
Abonyi Place in the Sydney suburb of Glenwood is named for him. Abonyi made a lap of honour on the MCG at half time of the 1998 World Cup qualifier against Iran.
