In response to Kelly Goodman's search for a 1-20 or 1-30 stepper relay,
these are the kind of things used in pinball machines of the 50's and
60's, before they went electronic. I would suggest checking the yellow
pages for pinball repair places to see what they may have.
These devices, as mentioned, can use either two pick magnets, one to
advance and one to retard, or some will use only one magnet to advance,
and when it reaches the maximum step count, will reset automatically.
The advance magnet could be wired to a push button switch, or a
microswitch that activates on the passage of a coin entering the coin
chute and the retard magnet could be connected to a vacuum switch
connected to the end of song hole. Of course some sort of interlock
would be needed during rewind so the retard magnet would not try to
count down on re-roll.