William Frederick Coates was born on 1 March 1866 at Strandtown, Belfast. He served an apprenticeship with Richardson Bros. & Co. linen merchants before taking up a career as stock broker.

Coates established W. F. Coates & Co., stockbrokers, in 1885. He entered the Belfast Corporation in 1902, when he was elected as a Councillor for Ormeau Ward and became Alderman for the same ward in 1916. In 1906, Coates served as High Sheriff of Belfast.

Coates was appointed as chairman of the Corporation Finance Committee in 1917, and served in that position until his death.

Coates was Lord Mayor when the first session of the Parliament of Northern Ireland took place. At that time the Lord Mayor of Belfast automatically became a member of the NI Senate (an upper house equivalent to the House of Lords). Coates was the first member sworn in to the Senate.

He was a keen motorist and one of the first owners of a modern car in Northern Ireland. Coates died on 19 January 1932, aged sixty-five, at his Carrickfergus residence.