You can't say that there's not until there isn't; they never tried.

In an alternative history, (where Lincoln was still elected, which he may well not have been, had the Democrats gotten their shit together at convention) the first thing that the South would want to do is actually have out the matter of slavery expanding into the new territories before Congress. My opinion is that South Carolina (and others) were simply too quick to secede and had done so as an obvious and direct result of Lincoln's winning the Election---they said as much in the document I quoted.

Anyway, what they should have done was waited until some action that would be hostile to the notion of keeping their own slaves in their own states happened. They were probably quite correct in seeing the writing on the wall in that, if slavery is not permitted in the new territories, and the new territories eventually become states, then MAYBE it becomes a Constitutional Amendment question. Even then, just based on the number of states there are now (and those who joined the Confederacy) such an Amendment, at best, would have been a very long way off.

In other words, the institution of slavery, within the Confederate States themselves, was not yet under any great direct threat. The problem that the South had was that slavery was not being permitted to expand.

Even without all of that, just by waiting for a year (or so) into Lincoln's term, you could eventually gather up enough support amongst the Southern states such that they all secede at once.

At that point, the Confederacy can send a delegation to Washington to discuss not only a peace treaty, but also discuss how they can maintain an alliance such that they will mutually defend one another against foreign attacks. The delegation could also address the idea of the Union pulling its troops out of the Confederate states in an orderly fashion.

The way it went down, South Carolina made no real effort (nor did any of the Confederate states) to engage in a peaceful effort by which they might even be recognized as sovereign by the United States. For further evidence of that, keep in mind that no other country in the world recognized the Confederacy as sovereign, either. By attacking without making any attempt to even be recognized first, after first cutting off Fort Sumter's supply lines, they'd committed an act of treason.

By the time the attack on Fort Sumter took place, South Carolina (and a few others) had already seceded for multiple months---and obviously, the United States had not attacked them. The Government of the United States still hadn't really figured out what it should be doing yet. Congress (what was left of them) was still debating with itself as to the question of whether or not the secessionists had the right to leave the Union, so they weren't to the point of being ready to negotiate with them yet.

At the time Fort Sumter was attacked, the United States hadn't even expelled the Senators Elected from the secessionist states yet. It wasn't until July of 1861, almost exactly three months after the attack on Fort Sumter, that the Senate essentially voted that the states did not have the right to secede...though I'm sure such vote had to do with the attack itself.

The question of the right to secession was very much on the table prior to that, and especially prior to the attack on Fort Sumter.