Coates reached his peak at the 1976 games in Innsbruck. He competed in five events, and apart from a 25th-place finish in the 500 m event, did no worse than 11th in the remaining four. He came sixth in the 10,000 m, eighth in the 1,500 m and tenth in the 5,000 m. It was only the second time that an Australian had placed in the top 10, and remained Australia's best result until 1994. His five skiing compatriots were less productive; they registered in 13 races between them and completed only seven due to crashes and disqualifications, with only one top 30 result.