South Carolina State Senator Lee Bright (R-Roebuck) and Representative Bill Chumley (R-Woodruff) say they will introduce a bill in 2014 to let parties close their primaries. See this story. South Carolina has always had open primaries, and has never before asked voters to choose a party (or independent status) on voter registration cards.
The article mentions that the Greenville County Republican Party recently was told by a U.S. District Court that it does not standing to win a closed primary via the court system, but the article does not mention that the Greenville County Republican Party has appealed this decision.
Although South Carolina law lets any qualified party choose whether to nominate by primary or convention, in practice, the qualified parties other than the Democratic and Republican Parties always nominate by convention, whereas the two major parties always nominate by primary.