IIRC about all the controller can drive would be an LED, works with SSR's but would need a driver transistor for a 4PDT relay coil. I kinda like TIP120 transistors, something like 3A output capable with a current gain of at least 1000. A ~1K Ohm resistor, TIP120 NPN Darlington transistor and 1N4001 diode should make a nice relay drive... or a lower power SSR could do the job.
IIRC the Basic Stamp outputs can sink or source. I think they can handle a little more current sinking than sourcing, though it's been years since I played with them.