Coster was born on 19 April 1920 in Eshowe, Kwa-Zulu-Natal, South Africa. He was educated at Maritzburg College, in Pietermaritzburg, KwaZulu-Natal, South Africa. After his matriculation at the school in 1936, he enlisted in the Special Service Battalion of the Union Defence Force (UDF) (of South Africa), and was commissioned into the South African Air Force (SAAF) on 6 September 1939. While flying a Curtis Tomahawk with 5 Squadron SAAF, he was shot down over North Africa by a Bf109 in 1942 and was a prisoner of war until May 1945.
After the war, he transferred to the South African army, and during 1952 attended the Royal Army Staff College at Camberley in England.
In 1955, he left the South African Permanent Force to join the Army of the Federation of Rhodesia and Nyasaland as a major. On the dissolution of the federation, he joined the Rhodesian Army, in which he rose to the rank of lieutenant general and was appointed as general officer commanding.
He retired from that post in 1972 as a lieutenant-general, having commanded the Rhodesian Army from 1968 to 1972. In 1959, he was made an Officer of the Order of the British Empire (OBE), received the Independence Decoration (Rhodesia) in 1965 and was awarded a Grand Officer of the Order of the Star of South Africa in 1981.
Keith married Molly Stanley in 1941, and two children, Steven and Judy, were born out of the marriage. After the death of his first wife, he married Millie Aherin in 1995.
He died peacefully on 5 June 2012 in Somerset West, South Africa.
- "Military old boys". Retrieved June 18, 2014.
- "Military Appointments", Africa Research Bulletin, 9, 1972
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