 Coates was born in Adelaide, South Australia, on 28 December 1932 to George Coates and his wife Gwenyth (née Begg).Educated at Ipswich Grammar School in Queensland, Coates graduated from the Royal Military College, Duntroon into the Royal Australian Armoured Corps in 1955.Coates was granted his first regimental posting in 1956 to the 1st Armoured Regiment.