Yes, there are three different stage plays, all written by Robert Penn Warren. The novel All the King's Men is based on Warren's play Proud Flesh. Warren later wrote another play, titled Willie Stark: His Rise and Fall, and adapted the novel into a play that he also called All the King's Men.Go to the web site robertpennwarren.com (linked below) for information on how to purchase a book that includes all three versions.
I also found two scripts from the movie versions. I've pasted links to them below.