Is it possible to reduce the resistance of a voltage source (coil)? If yes, how can I do that?
Caveat: I think you would be best off using a different design of coil, but if you want a direct answer to the question you asked:

Immerse the coil in liquid nitrogen.

This will reduce its resistance by a factor of 70 or so. The coil will also stay cold and low resistance for a few minutes after draining away the nitrogen, if the presence of the liquid would interfere with your experiment.

This is very much a one-off solution, you wouldn't want to build a product with it, but it sounds like this is a one off experiment, so it might work for you.  

Note that liquid nitrogen is a somewhat dangerous substance. It can cause severe burns, it can cause remarkably large explosions if stored in sealed vessels, and if you use/spill a lot at once you can drown in the resulting nitrogen gas. Find someone with experience handling it to show you the ropes.