how can you submerge 6 eggs in one cup of liquid?

As Kate said, a ziplock bag would work, but I've just done it in a glad container with a lid. I open it and spin the eggs a bit to make sure all of the eggs are marinated. It works great.

You could try a Ziplock bag perhaps? You could then turn it about to ensure the eggs stayed coated in the liquid, especially if you squeezed some of the excess air out of the bag.