Onishi was born in Kyoto on April 18, 1943. After graduating from Kyoto University of Education, he joined Mitsubishi Motors in 1967. The club won Japan Soccer League champions in 1969 and 1973. The club also won 1971 and 1973 Emperor's Cup. He retired in 1974. He played 83 games in the league.
After retirement, Onishi became a manager for Toshiba in 1981. He managed until 1985–86 season. In 2002, he signed with Thespa Kusatsu and became a general manager. From November 2005, he also served as president.