Coryton was the second son of John Coryton, of West Newton Ferrers, St Mellion, Cornwall, and his first wife, Elizabeth Mills. In 1661, his father was created a baronet.[2]
In 1688, he married Susanna Littleton, daughter of Sir Edward Littleton, 2nd Baronet. They had a son, John, and daughter, Susanna. He inherited the baronetcy from his elder brother, John, who died without an heir in July 1690.[1] After her death in 1695, he married Sarah Williams, widow of Thomas Williams.[1]