As I was not even thinking about creating a superconductor out of copper, but just lowering the resistance a measurable amout for testing purposes to see if there really was a measurable difference. I had the thought that if a secondary was filled with dry ice, it would be easy to handle not being liquid, and the CO2 vapors will mostly follow the primary down the side being heavier than air. This also can quench some of the corona, as well as drop around the primary winding, cooling that as well.
Gary is correct that the biggest losses are in the spark gap and primary circuit, so a SG coil may only see some improvement with a cooler temperature. I would assume then that the greatest gains would be found in an SSTC setup where switching losses are at the minimum achievable. I had only brought up the superconductor name because it is a research that shows a change in resistance of materials at lower temperatures.