I agree with Caferacermike, the coil needs to be metal to work best but unfortunately titanium is expensive, aluminum doesn't come in hollowed tubing very easily, and copper is awful for a reef system.
Ric, yes copper is a bad choice. Saltwater corrodes copper quite readily and it will put copper particles into your tank effectively killing all crustacea, including copepods and micro-crustacea, and the fauna of your tank will be heavily affected. Copper is often used for fish treatments so I doubt a little copper would do much harm to a fish but in this setting it would not be good at all.
If all else fails, you might find an aluminum box to put inside the dorm fridge and have it act as a sump/chiller, although your surface area will be far less than if using tubing making this setup much less efficient.
Just some ideas.
-Steve