Back in the day, you used to order a special phone company circuit for pay phones, but modern pay phones will connect to a standard analog line. That means you can plug a payphone into an FXS port on your Cisco System (using an ATA, or a VG gateway). However, it's recommended to order a direct line from the telco for your payphone, instead of connecting it behind your Cisco switch (for fraud prevention purposes).
Cisco doesn't manufacture payphones, so you'll need to go with a third party manufacturer. Just google "payphones," and you should find plenty in the range of a few hundred dollars or less. Any quality third party manufacturer should work fine.
Good luck.
Kelly
kmaloy@isaso.net