I can't say for sure, but I would hesitate to say there were absolutely no specially designed Jim Crow Car cars. When the General toured the USA in the 1960's, she routinely carried a former L&N Jim Crow car. I was under the impression that car had been built for the purpose, but perhaps it was a shop modification. I understand it still exists in a Museum. I believe the location is New Haven, KY. Somebody can correct me if I am wrong.
The book Rails Through Dixie by John Krause and H. Reid (Golden West, 1965) has photos of Jim Crow combines on the Wadley Southern and Sylvania Central. Lucius Beebe's Mixed Train Daily (Howell-North, 1947) also has several photos of Jim Crow combines on a variety of lines including the Sandersville, Louisville & Wadley, Wadley Southern, and Sylvania Central. The Talbotton's single coach is pictured, It shows no external evidence of having separate sections, although it probably did. Both of these books are long-out-of-print classics that can sometimes be found at railroad shows, used book dealers, or on ebay. I didn't see any Tallulah Falls photos in any of these books, nor in H. Reid's Extra South.
I suspect you could build a credible Jim Crow combine using a LaBelle coach kit, or one of the old Ambroid (Northeastern) kits, the latter being out of production (I think). There are also plastic cars that could provide a good starting point.
Please keep in mind the fact that this is a very sensitive topic. I recall a bit of controversy over the depiction of a Confederate Battle Flag on a model railroad several years ago. It was presented in historical context, but it still made a lot of people uneasy. It wouldn't be hard to give offense if you're not very careful of people's sensibilities. While many people think this is ancient history, it is very real to many good Americans who experienced this humiliation, and remember it vividly. Frankly, I'm not sure I would feel very good about getting into the subject. I'll stick with modeling the North, which had failings and troubles enough of their own.