What power supply current rating can replace 6 1.5 V C batteries?
You need to know the current requirement for the CD player to work correctly. Use a digital multimeter (DMM) to measure the current that is drawn by the device from a fresh set of six C cells. Make sure that the CD player is running with the disk motor active and the sound level turned up to maximum.

You could also use a bench power supply that is set to a nominal 9V and use test leads to clip that supply into CD player at the end contacts of the six cell battery compartment and connected to the DMM in current measurement mode. When using this method make sure to use a bench supply that is obviously capable of delivering all the current that the CD player would need (in other words a 3A to 4A supply and not some whimpy little 9V wall wart rated at 200mA).

Once you have the current measurement I would multiply it by 1.5 for reserve capacity and you will have an appropriate selection for a 9V power supply at that current level of capability.