I'm trying to think how popular sports would be in the CSA. I can't think of a single sport invented in the CSA (football as we know it started in New Jersey, baseball in New York, basketball in New England and hockey in Canada) and there was a bill before the governor of Georgia to outlaw football. He vetoed it based on an impassioned plea from the mother of a young man killed while playing the sport; if it's seen as a Yanker sport from outside Confederate lands, that governor may not view the game so nicely and sign the bill. And if he does, other states will probably follow suit. As such, football will be niche at best in the CSA, and sports may not catch on the way they did OTL (other than football, there isn't a whole lot of market for sports outside big cities, and professional leagues will probably hesitate to enter the CSA; we can certainly butterfly away basketball's popularity in North Carolina since there are other hotbeds such as Indiana and Kentucky that would remain firmly Union.)
Furthermore, the biggest catalyst to sports taking off in America was the reduction of the work week. With slavery still legal in the CSA, cutting the work week back, even to 60 hours, OTL's magic number, will be many years off. So while the USA has manufacturing advantages and is an industrial center for steel and cars, the CSA is scraping tooth-and-nail for whatever it can find and is still likely focusing on industrializing agriculture. So with so few jobs, so many people wanting them, and slaves to fill in gaps, the CSA won't have the time or ability to conduct leisure activities.
And assuming the World Wars happen similarly to OTL and the CSA joins the Allies (they may believe in slavery and/or segregation but they'll see themselves as above the Nazis) then with times improving back home, people in the CSA may take a liking to some sports. It's hard to see what sports they would prefer, but plenty of things such as racial politics and a lack of tradition would hinder CSA sports programs. They would lag far behind the USA in most Olympic and professional sports, and if a CSA league got started up, it would be seen as inferior. Why would someone want to play football in Atlanta when Philadelphia pays better? And the USA would get a lot of CSA black defectors - sure, it will cause tension, but overall it will be good for the quality of the product. And with no legal protections in the CSA for black athletes, many of them will not want to stay; bear in mind it was a post-Civil War Amendment - one that won't exist in the CSA - that ended segregation. And passing legal protections for black athletes in the CSA will be nigh impossible. So expect a lot of blacks to migrate north and west, with many border areas being heavily black.
In short, CSA sports will be very white, have no tradition, and constantly be second-best. And the interest will be spotty. And that's if they're allowed to compete at all.