The 1919 Cincinnati Reds World Series program was reprinted by Robert Opie as the first volume in a series of reprints of World Series programs. I believe only 1,000 were made but they're not super scarce and can be found on Ebay. (As of now there's one copy on the auction site, the seller is asking $27.95 as a "Buy It Now.")
Another option is to get a copy of the book
Souvenir Programs of Five Great World Series, 1914, 1917, 1919, 1926, 1934, published in 1980 by Dover Books. As implied by the title, the 1919 Reds program is one of the programs included in the book (curiously, sourced from an Opie reprint rather than an original). What makes this book a must-have is that the 1926 program included in the book is the Yankees' version, which was
not reprinted by Opie. It's available on
Amazon for less than $10.00 and, in my opinion, is well worth it.