The problem is a PIC12C508 requires up to 50mA from Vpp during programming and Vpp mustn't drop below 12.75V during programming. (see
http://ww1.microchip.com/downloads/en/DeviceDoc/30557g.pdf )
Most cheap / minimal / DIY programmers cant hold Vpp at 13V +/-0.25V reliably with a 50mA pulsed load on it.
IIRC the PIC12C508 and the PIC12F508 are binary compatible and apart from the different programming characteristics, and the pin 5 (GP2/T0CKI) input characteristic, are electrically compatible.
(GP2/T0CKI is a Schmidt trigger input on the 'C508 but an ordinary CMOS input with TTL thresholds on the 'F508.) Therefore, in most cases, you can simply use a more modern programmer that doesn't support EPROM memory PIC1xC... parts, to flash a PIC12F508 with your PIC12C508 code, and use it in place of the 'C508.