Coe was born Percy Newbold Coe in Kingston, Surrey, the eldest child of Violet (née Newbold) and Percy Coe Sr (1893–1974). Coe had a younger brother, Peter, who died in infancy in 1928, and took on his brother's first name as a dedication to him. Coe's first marriage ended in divorce, and in 1954 he married Tina Angela Lal, with whom he had four children including Sebastian Coe.
As an engineer, Coe became dissatisfied with the athletics coaching offered to his son Sebastian at his first club, Hallamshire Harriers. This training was based on the principles propounded by the New Zealand coach Arthur Lydiard, and involved a substantial amount of long-distance running. By contrast, Coe took the view that "long slow training turned you into a long slow runner", and adopted a system of speed-endurance training involving fast repetitions with short recoveries, based on the ideas of the German coach Woldemar Gerschler. In addition to coaching his son Sebastian, Peter Coe also coached Wendy Smith-Sly, who placed second in the 3000 metres at the 1984 Summer Olympics.
Coe's second wife, and mother of four of his five children, Tina Angela Coe (née Lal), died in Hammersmith and Fulham, London, in 2005, aged 75. Peter Coe died in 2008, aged 88.