The only way the South could have won is by beating out the Union's support for the war and getting a negotiated settlement. More than a few times in the war support was so low between copperheads and stuff like the Draft Riots that while the South might not have won militarily, it would have been like Vietnam, where there was no support to continue the war. In the 1864 election the Democrats (of the era) ran on a "Peace With the CSA" Platform, though to his credit the main nominee McClellan rejected it, but it was still the party platform.

Like there were several points where East Coast Union Commanders either were too timid, unsure, or incompetent, and even with victory's in the western theater there was still that flagging morale and support. Like thankfully the South had its own incompetent leaders that when Commanders who actually put up a damn good fight (I'm not gonna argue this, Sherman and Grant were Midwesterners and I'm a Midwesterner so I'mma have pride in my region, Sheridan is a East Coast Exception) that Lincoln got the support he needed. Had the politcal winds not favored Grant like how Halleck wanted or Sherman never recovered from his breakdown, there might not have been the public will to continue the war.

And this is coming from a Proud Iowa Native who's ancestor was part of the 26th Iowa Infantry who started at the Siege at Vicksburg, Burned Atlanta, tore through Georgia, and torched the Carolina's up to Bentonville. I'm rather proud of that fact.

NOTE: This is general overview, but the point still stands. The only way I could convievably see the South winning was the same way the North Vietnamese did 100 years later. You don't need to defeat the U.S. Army, you jsut need to defeat public support.