When shipping shrooms, zoos, and the like, most people will just use priority mail. That's what I have done in the past. The best way to do it is to use a thermos like you put coffee in...you can get them pretty cheap at Wal Mart.
You put some water in a bag, put in the coral and the seal the bag really well (tie a not, use rubber bands, etc). Don't use ziploc bags they always leak! Then you put the sealed bag in another bag and then you seal that bag.
Then you put it in the thermos, put it in a box with propper packaging "stuff" and send it on it's way via US Priority Mail. They will usually ask if there are liquids in the package...you just smile and say "no."
The thermos keeps the water from experiencing extreme temperature shifts. Plus it's actually only supposed to be low 80's to mid 80's here beginning of next week so it would be a perfect time to ship.
Want to give it a try? Email me at brian.rish at earthlink.net and we can discuss more.