His championship career at the senior level with the Limerick county team spanned sixteen years from 1918 until 1934.
[1] McConkey first played competitive hurling with the St Patrick's club in Limerick.
He later joined the Young Irelands club and won five county senior championship medals between 1920 and 1932.
Impressive displays at the club level brought McConkey to the attention of the Limerick senior team selectors and he was quickly added to the team.
After being chosen on the Munster inter-provincial team for the first time in 1927, McConkey was an automatic choice on the panel for two seasons.