It didn't matter if it was FDR in 1936 or Cox in 1920, South Carolina was always giving the Democrat about 95% of its vote. I don't think a Republican party even existed in the state until the 1950s. For all the talk of polarization that's going around, I don't see a state ever being as one sided as South Carolina was for all those years.
Don't forget Mississippi. Between 1896 and 1948, the GOP broke 10 percent in Mississippi only twice: in 1920 (14 percent) and 1928 (18 percent).
Even Vermont was never as one-sided as Mississippi and South Carolina when it was Republican. The highest percentage any GOP presidential candidate got in VT was when McKinley got 80% in 1896, followed by Coolidge's 78% in 1924.