I pack mine in thick wads of newspaper and pack them tightly into a priorty shipping box from the PO, the one that is a little bit thicker, like a cinder block size, not flat like a paving tile. I always get delivery confirmation too. If the eggs are not enough to fill the box so that nothing can move, keep packing wads of newspaper around the eggs, trying to keep the eggs away from the sides of the carton. Hopefully others will share their methods. There are a lot of different ways to do it right. Good luck!
The ones I got were individually bubble wrapped. Then I think they were put inside a ziplock bag. Can't remember if it was open or shut (seems like they would need air?) Maybe it was folded and taped. I really can't recall exactly.
Anyway, the two packages were then placed in the box with a thick layer of wadded newspaper above, below and around. As the other poster said, it was the bigger box, like cinder block size. She also marked the box as to the contents and warnings not to x-ray, etc.
No problems in transit, all eggs of one breed hatched though none of the other did. Most likely an incubation problem though.
I use the medium flat rate box even if it is just a few eggs as the smaller boxes get tossed around too much in the PO. . I re-enforce it with cardboard on all sides and bottom, then I found that a cardboard egg carton fits inside perfectly. I can put up to 3 cartons into the box if on their side, and 2 if right side up. I wrap each egg in tissue and I glue cardboard to the inside of the lid of each carton for added strength I make sure there is no movement in the egg cartons at all and that they are closed tight. I use newspaper for padding bellow and above and then add another piece of cardboard on top before closing. I rarely have eggs break if ever this way, and can get up to 32 eggs out in one shot. The box weighs about 3-4 lbs when I am done and is so strong that it would take a lot to damage it.
oh and FYI putting do not Xray on any box pretty much garantees it WILL get x-rayed according to the people I know who work at the PO. The best thing to do is put "Live Embryos fragile" on the box and ask the po person to stamp it with the perishable stamp. I never put that they are eggs, I would rather them think they are human embryos or not know what they are so they handle them with a bit more care.