He played for Hillhead HSFP.[2]
Cotter was named in the Scotland Possibles side on 13 January 1934. Batting for selection, was his opponent on the Scotland Probables side Kenneth Jackson from Oxford University.
The Aberdeen Press and Journal noted that day:[3]
Cotter is a player of exceptional merit, he has, indeed, that quality all-roundness which seems to characterise all great players. A grand fullback, clever centre, he is also an accomplished stand-off half. Jackson will require to be his best to outshine Cotter.
He captained Glasgow District in their 1934 inter-city match against Edinburgh District.[2]
He was capped by Scotland twice in 1934.[4]
Cotter did well in his first game against Ireland. from 3 March 1934 issue of the Illustrated Sporting and Dramatic News:[5]
The new outside half, Cotter, the young Glasgow clergyman, created a most favourable impression, hitting things off quite well in his first partnership with that splendid player Logan, and the Scots were much better served at centre, where Dick and Lind, especially the former, were in great form.
He went on to coach Langholm.