Scarlett learned about abortion through Mamie Bart, but she didn't learn about contraception, or perhaps she wouldn't be so quick to kick Rhett out of her bed. One presumes, Rhett knew about contraception, but chose not to share this information with his wife. It's something I always wondered about. Here are some links to contraception during the mid-nineteenth century.
Percy Skuy, a former President of Ortho, had one of the largest collections of contraception old and new in the world. His collection is housed at Case Western University, who in turned made some webpages on the history of contraception, including soldiers in the Civil War. Only Union soldiers are mentioned. There is also a page on Condoms and Sponges, both of which were available during the 1800's.
Contraception: Civil War Style provides another overview of contraception options in the 1800s.
Charles Knowlton wrote one of the early works on population control, Fruits of Philosophy , which included information on contraception, though the efficacy of the options seem questionable.
Planned Parenthood has a great paper A History of Birth Control Methods, which cites sources and provides information on a variety of methods old and new.