[Mr.Lizard]

I would think you could wrap the coral in the damp paper towels as noted, but then place them in a sealed/rubber banded plastic bag with a bit of air to aid in cushioning....then some styro peanuts or bubble wrap to isolate the container within the styro-insulated shipping container. (cooling or heat pads as determined to be necessary, but you'd have to isolate them from direct contact with the specimens) It probably would work best individually rather than more than one at a time in any one bag, I'd think.
I like the ziploc container idea- several corals could be packed individually with towel and a bit of air like I was saying, and then packed in the rigid plastic container for extra protection with any heat/cool packs deemed necessary outside that- I believe keeping the heat/cool from direct contact with the container would be adviseable to avoid hot/cool spots.