Shoot, it must have a big honking coil in it.
Well we still need a heavier duty resistor. It looks like the resistor will be dissipating about 5.8 watts so you may even want to go to a 10 watt resistor. Radio Shack or other electronic stores will have them.
If they don't have the exact one you want then you can connect multiple resistors to get there.
I'm a little concerned that with the relay and resistor drawing this much current, the capacitor I suggested may be on the small side. If so, I suspect the symptom you'll get will be a singing or chattering relay at low levels of power dumping. If this happens just add one or more capacitors in parrallel to the original one to fix it. Be sure all of the capacitors have at least a 100volt rating.