There is no definite time when the player piano was first developed.
The first patent on a pneumatically automatic piano was given in 1863 to a Frenchman named Forneaux. He named his contraption the "Pianista."
"Push-up-players", as they generically became known, were popular for a short time, about 1900 to 1905.
In 1923, the "Pianola", a brand name of player piano was manufactured by the Aeolian Corporation.
http://cdelker.tripod.com/music/player.htmlIn the pre-electronic age, inspired by actress Hedy Lamarr, George Antheil designed a mechanical player-piano-type device that would provide the pattern for the sender and receiver of an anti-jamming radio control for torpedoes. On Aug. 11, 1942, they were awarded patent 2,292,387 for their "Secret Communication System."
http://www.usatoday.com/tech/columnist/kevinmaney/2002-09-03-maney_x.htmAccording to another site, the concept of the player piano originated in the US about 100 years ago. They were called "Piano Players."
http://www.musicalmuseum.co.uk/player.htmlAccording to yet another source, in 1887, the player piano was invented in the US. This instrument could record a performance on a paper roll. This roll could be copied and manufactured and distributed to people with player pianos to reproduce the performance, much like MIDI files are traded today.
http://www.synthmuseum.com/magazine/time0010.htmlWho knew?