http://www.baseball-reference.com/bullpen/Pitcher - scroll down to "Historical Usage."
According to this source, you are 10 years before the time that "full-time relief pitchers became common." I would play by house rules that reflect the times if that is the case in your game.
However, if this is a fictional game that you just chose to date as 1929, I know of no reason why the game would be aware of this historical fact. Of course, if you are playing somebody's quickstart, then that would be the answer perhaps.