A good source for electromechanical coin counters and the like is
someone who collects and restores pinball machines, or who supplies
hardware to those who do.

Most pin games made between 1950 and 1978 have a "replay unit" or
"game counter" stepping switch with two coils, one to step up and
another to step down, and a switch that cuts off the fun when it
reaches zero.  As a plus, an attached wheel has numbers printed on
its rim that show how many plays remain.  Most units can handle up
to 10, or 20, or even 40 plays.

Depending on the make and year replay unit you come up with,
you'll need 24, 30, or 50 volts AC to operate the coils, meaning
a transformer.

By the way, I have an up-down counter from a very early photocopy
machine, that uses pneumatics to step up and down, and other player-
piano technology to control the copier.  I probably still have the
vacuum pump, which, other than being of cast aluminum frame, looks
and works exactly like the one in my Weber Duo-Art grand!

Mike Knudsen