I'm afraid I can't offer much advice, except maybe enough to help get you started...
First, I would call ATF (seriously
) and ask them to list for you all of the type 09 and 10 FFL's in SC. There may be zero. That's ok...
Try these online lists:
http://rkmerting.com/south-carolina-gun-shops/
http://carolinaguntrusts.com/sc-class-iii-dealers/
Even if there are no DD FFL's, call around and see if anyone is knowledgeable about M203 sales. You'll probably get tired of doing this, and get asked if you want a flare launcher unbearably, but you may strike gold.
If you don't strike gold, pick your favorite "normal" class II or III SOT, and advise them that it is OK with the ATF if they transfer one DD per year, especially if there are no DD SOT dealers in your area. This would work just as if they were a DD SOT for the purposes of this once annual transfer. When the place with the DD you want sends in the Form 3 to ATF, just have the sender/transferor include a note on the transferee's (the incoming SOT you're using as a dealer) letterhead stating that the DD is for you, their customer, and you wish to have it transferred to you on a Form 4 for individual use, and this will be their once annual DD transfer. (It may help for the shop to call NFA Branch and have a chat with whomever their normal examiner is.)
That's pretty much it. You can have a DD shipped to them from any state, new from LMT, etc.
The other path you could take to M203 ownership would be purchasing a receiver without a barrel (this would just be a normal Title I firearm), do the 4473 (as "other") for it, then file a Form 1 to make a DD yourself. You'd then have to engrave the receiver with your making info, but once approved, just order a 40mm M203 barrel and slide it right on there. If you can find a reasonably priced smooth bore 37mm M203 barrel (and good luck with that
) in the meantime, then you could certainly play with that until your F1 comes back approved. Don't own a 40mm barrel for it until then though.