why did south carolina change their vote for independence?

Answer 1

"[On July 1] Mr. Edward Rutledge of South Carolina . .. requested the determination might be put off to the next day, as he believed his colleagues, though they disapproved of the resolution, would then join in it for the sake of unanimity."
http://www.britannica.com/eb/article-9116901/Document-Thomas-Jefferson-Debate-on-Independence

So says Jefferson in his autobiography (the actual congressional record of these proceedings is very sketchy).

The key is in the last few words "for the sake of unanimity". In fact, ALL the delegations by this time understood that such a resolution was almost unavoidable. The debates in June of 1776 had focused on methods and timing. So South Carolina (where, along with Georgia, the Loyalists were strongest) had held hopes of reconciliation longer than others, and wanted to defer the question as long as possible. But they saw that the question was succeeding (the overall vote on July 1 was 9 states for, 2 against [SC and Pennsylvania by one vote], Delaware tied and New York abstaining). So better to unify behind it.

(There was a similar feeling in the Pennsylvania delegation [initially 4-3 against], and so Dickinson and Morris --two "No" votes-- abstained from voting on July 2, which reversed that delegation's vote. And Caesar Rodney rushed 80 miles from Delaware to break their tie in favor of the resolution. New York wanted to support it, but abstained, lacking the authorization... though they finally received permission to vote "Yes" on July 9.)