There's been a lot of success, especially with soft corals that have strong mucous reactions, with damp shipping. The coral frag is wrapped in a wet paper towel and then placed in a plastic bag, filled with air. This bag is then shipped in a styro lined box, to insulate temperature. This cuts down on shipping weight and also cuts down on the coral producing lots of amounts of mucous. From everything I've read, this is one of the best ways to ship soft corals IF the coral can go from tank to tank in under 18 hours.
Otherwise, double bagged, in a bag of 1/3 water and 2/3 air. Bag placed in a styro lined box, with heat pack taped to the lid of the box, to keep the heat pack from coming into contact with bag. You'll still want to ship next day, if possible. You can also attach the coral frag to a piece of styrofoam and hang it upside down, in the bag. The styrofoam floats, suspending the coral below it, in the water. This keeps the coral from coming into contact with the plastic bag, which irritates it.
Some corals, such as Zoanthids and hardier leather corals, commonly do fine with 2 day shipping, as long as there are no extremes in heat or cold.
Lately, a lot of success has also been had using the damp method with Zoanthids. I'm considering trying it with a few different corals, myself.
The reason people have been experimenting with the damn method is because it's been shown that a lot of shipping mortality is due to the coral being submerged in it's own chemical slime, in water and from being irritated by coming into contact with the bag.