Dude whatever you do don't put 110V through a PCI card :P
If you try and run a 110V pump from 12V it won't work, it simply won't draw enough current to operate.
You might be able to get 12V DC motors for pumps, try perhaps a pet store for a fish tank pump. They should come with a transformer and rectifier so you do not need to run it off your power supply, i'm not sure what kind of current they draw but you will probably need a fairly hefty (400W+) power supply to be able to do it.
Actually, an AC appliance won't run from a DC source without an inverter. To go from your 220 vac to 12 vdc you could use a transformer paired with a full bridge rectifier. Of course, buying a wall transformer would probably be a whole heck of a lot easier. They're cheap and fairly common. It should take just a little splicing to connect it to the PCI relay and the pump.
This ones rated at 1 amp @ 12v, so it's probably good enough for your application, although you will want to check the power rating on the pump. Also, I see that's it's a British style plug so you might have to convert plug types, but that shouldn't be to big of a deal.