Coogan was born in Monkstown, County Dublin in 1935, the first of three children born to Beatrice (née Toal) and Ned Coogan. Ned (sometimes referred to as "Eamonn Ó Cuagain"), a native of Kilkenny, was an Irish Republican Army volunteer during the War of Independence and later served as the first Deputy Commissioner of the newly established Garda Síochána, then a Fine Gael TD for the Kilkenny constituency. Beatrice Toal, the daughter of a policeman, was a Dublin socialite who was crowned "Dublin's Civic Queen of Beauty" in 1927. She wrote for the "Evening Herald" and took part in various productions in the Abbey Theatre and Radio Éireann. Coogan spent many summer holidays in the town of Castlecomer in County Kilkenny, his father's home town.