Actually no. Wild Bill Hickok was not a coward. He was an extrememly good scout for the Army, and frequently a sheriff or marshall. There is no proof he ever shot anyone in the back. He was a gambler (not notorious for it, unless you consider being good at it notorious), and he was not a drunk. His enemies spread rumors of back shooting, STDs, drunkeness, and other unsavory things.
He was shot in the back while gambling (it is where the Dead Man's Hand comes from). He did suffer from Glaucoma or more likely Trachoma. This caused a drastic decline in his marksmanship. Because of that he fell on hard times as he couldn't get a job as sheriff or scout. Look him up. The History Channel did a series on "The Real West" a few years back. They did a good job telling about him.