Aloha! Roy,
With any other Nikon bin, the solution would be simple - buy a pair of Bushwacker covers. However, with the EDG II, those big bumps they made near the end of the objectives for the straps that hold on the covers (but apparently don't prevent them from "flipping out" :eek!

don't leave much clearance for Bushwackers.
Here's what they look like (though this is not the right size for the 42mm EDG):
http://www.eagleoptics.com/binocular-accessories/quake/bushwacker-optic-cover-size-4-matte-black
You might still be able to get Bushwackers on the "stubs," but you probably won't be able to push them all the way on. That's how it was with my 8x32 LX, which had stubs for barrels. They stayed put, but sometimes they would tilt inward and I'd have to straighten them out.
The other solution is to tighten the fit of the flip covers, which appear to fit inside the objective housings. I tried building up tape around the cups with a pair of Nikons that had that set up (XL Zooms), but the glue eventually dries up and comes loose. What I have had success with is foam insulation strips that go around windows, which you can buy at the hardware store, or you can here, because it gets cold in the winter (or at least it used to, it's October in PA, and the leaves are just starting to turn colors, only about 20% of the trees, and the high temp. for today is going to be 78* F. Usually, by Oct. the leaves have turned color and are starting to fall.)
So you have two options. Take off the OEM covers and replace them with Bushwackers and hope they fit, or build up the space inside the covers with insulation tape or something similar that provides a tighter fit.
Aloha! again,
<B>