What's a good EEPROM replacement for a 27C256/29C256?
I believe the 29Cxxx series is now mostly flash memory.

Digi-Key appears to have several thousand of the 32Kx8 AT28C256 EEPROM's, which are almost the same pinout as the 27C256, and appear to be supported by your programmer.  You didn't say which package you are using, I assuming it is a 28-pin DIP.  There is also a 8Kx8 version of the same chip with a compatible pinout (unused address lines are no connects).  It is a little cheaper in price, and also in stock.