I have not done it yet, but I have read a lot about shipping. Some say "dry" shipping is the best way -- where you wrap the corals in moist paper towels/newspaper. Some says it's a terrible idea. From what I can discern as consensus, it really depends on the specimen you are sending and how far it has to go.
For shipper, I know USPS in some delivery areas has a hold-at-office next-day option, where the package will arrive at the local post office the next day for pickup by the recipient. Not available in all areas, though.
Good luck!