He was born at Hartsville, South Carolina on October 24, 1872. He graduated from South Carolina College in 1894 and took postgraduate courses at Johns Hopkins University and in Germany. He taught for several years in the summer schools of the Brooklyn Institute of Arts and Sciences, at Cold Spring Harbor, L. I., and in 1902 became associate professor of botany at the University of North Carolina. He established the Coker Arboretum in 1903. He was made professor in 1907 and Kenan professor of botany in 1920. In 1903, he was chief of the botanic staff of the Bahama Expedition of the Geographical Society of Baltimore. Professor Coker was a member of many scientific societies and the author of The Plant Life of Hartsville, S. C. (1912); The Trees of North Carolina (with H. R. Totten) (1916); and The Saprolegniaceae of the United States (1921). Besides these he contributed numerous articles on morphology and botany to scientific journals. He died on June 26, 1953 and was buried on June 29, 1953.