The song that is most directly about Joe DiMaggio is Joltin’ Joe DiMaggio, written by Alan Courtney and Ben Homer, and performed by Les Brown.
Other songs about ballplayers:
Did You See Jackie Robinson Hit That Ball? , written by Buddy Johnson and performed by Count Basie.
Say Hey (The Willie Mays Song), performed by The Treniers and written by ???
Willie, Mickey and the Duke (Talkin’ Baseball), written and performed by Terry Cashman. Along with the players in the title, this one also mentions Bobby Thomson, Yogi Berra, Ted Kluszewski, Roy Campanella, Stan Musial, Bob Feller, Phil Rizzuto, Sal Maglie, Don Newcombe, Casey Stengel, Hank Aaron, Ralph Kiner, Eddie Gaedel, Ted Williams, Mel Parnell, George Brett, Bobby Bonds, Pete Rose, Rusty Staub, Grover Cleveland Alexander (and Ronald Reagan by implication), Reggie Jackson, Dan Quisenberry, Rod Carew, Gaylord Perry, Tom Seaver, Steve Garvey, Mike Schmidt and Vida Blue.
Van Lingle Mungo, written and performed by Dave Frishberg, is simply a list of the names of many ballplayers set to music.
I Love Mickey, performed by Teresa Brewer and Mickey Mantle, and written by ???
Slide, Kelly, Slide, written by John W. Kelly about the 19th century baseball star Mike “King” Kelly (no relation to the songwriter).