Cobbe was born in Mountmellick, County Laois, Ireland on 26 January 1934.
[2][3] From the St. Patrick's club, Cobbe first came to prominence on the inter-county scene with the Limerick junior team that overcame London to win the 1955 All-Ireland Junior Championship.
Promotion to the senior side followed, with Cobbe lining out in the forwards when Limerick surprised Clare to win the 1955 Munster Championship.
[4] The team, labelled "Mackey's Greyhounds" after their trainer Mick Mackey, were subsequently beaten by eventual champions Wexford in the All-Ireland semi-final.
[5] Cobbe continued playing for Limerick until the 1960s, by which time he had also won two Railway Cup medals with Munster.