Cogan was born in Cork, where he was a choirboy and vicar choral at St Fin Barre's Cathedral.
In 1772, he was appointed a stipendiary at Christ Church Cathedral, Dublin, but left the post a few months later due to ill health.
He was an active participant in Dublin's musical life for many years including performances in the annual "Commemoration of Handel" festivals at the Rotunda and at various charity concerts in both Catholic and Protestant churches.
Cogan was a much sought-after teacher and counted among his pupils a number of noteworthy names in Irish musical history such as Michael Kelly, Thomas Moore, P.K.
Cogan enjoyed a long and prosperous life; he died at the home of his son-in-law, Patrick Clinton, at 14 Dominick Street, Dublin, and is buried in Glasnevin cemetery.