I would do it with a PIC, but there are many different ways. You could use an old UART, I seem to remember the 6402 was one?, or you could use the handshake lines to feed a relay via a simple driver.
Personally I would advise a PIC solution, where you could easily (and more reliably) control the switching on and off of the relay - either by simple characters, or even text strings.
My RS232 PIC tutorials show how to do this with LED's, you would just need to replace the LED's with transistor drivers feeding relays.