Joe Paul Brewster (October 26, 1935 – August 8, 2021) was an American football coach. He served as the head football coach at Austin Peay State University from 1988 to 1989, compiling a record of 3–19. A native of Lenoir City, Tennessee, Brewster earned a bachelor's degree in 1958 and a master's degree in 1967 at East Tennessee State University. He came to Austin Peay in 1981 as an assistant coach under his predecessor as head coach, Emory Hale.[1]