hi Paul,
Put the biggest egg box that you can fit in there and fill it with as much vermiculite, perlite, or both that the box will hold while still having room for the eggs. The egg box should be sealed so the moisture level doesn't fluctuate too much. You will allow for enough gas exchange when you check on the eggs every couple of days. Also, make sure the medium is only slightly damp, so that it just barely clumps together when squeezed, too much water will cause the eggs to balloon up and die. They should not appear really taut or swollen with water.
Will
PS - I really don't have any rats to spare, in fact, I'm looking to expand my own colony.