Alan,
A portrait of Col Pinckney in the Smithsonian shows dark blue coat faced scarlet, with the distinctive Carolina cap with the crescent badge on the front. However, x-ray examination of the painting shows blue faced buff, which was the original uniform of the 1st SC (his red-faced-black pre-war militia uniform is under that, so the portrait was re-painted at least twice).
There is also a report from 1778 indicating that the 2nd SC was wearing the same uniform as the 1st (interestingly, it is described a "black faced with red"; some men were also noted as wearing "white frocks" (be aware that this is not necessarily the same as hunting shirts).
The 3rd SC initially wore blue faced white (1775), but in 1778 are noted as having "different dress". This could mean either different from the 1st and 2nd, or that the men wore civilian clothing, or a mix of uniforms. Caps were noted as being worn (this was post-78).
The 4th SC was an artillery unit, and wore blue faced red, with blue small clothes in winter and white in summer.
The 5th and 6th SC were both rifle regiments and disbanded early in 1780. In 1778, officers of the 5th were noted as wearing red coats faced black (the pre-war Charleston Militia uniform, as per Pinckney above). However, Major Huger – who was killed in May 1779 – was painted during his life wearing blue faced red, silver buttons and epaulettes, and a normal cocked hat. The 6th were described in 1778 as "militia grenadiers" (which usually means experienced men, not actual grenadiers) in "proper dress and caps".
[All the above from Katcher's uniforms of the COntinental Army.]
Hope that helps a little.