Did the Southern States make any attempt to secede from the Union through an act of Congress?

The answer is: It depends on your point of view.

In regard to 'resolving the conflict peacefully' - The Southerners never fully believed initially that the North would go to war for the sake of abolition.

The issue of the day was: Did secession require an act of Congress to legalise it? The Constitution never mentions secession at all or even a perpetual Union. I believe this is what's referred to as 'state's rights' or 'compact theory'.

The belief was the various states delegated certain responsibilities to the central (federal) government, and everything else was pretty much left up to them. As the Constitution made no mention of the right to secede, and thus the States felt that annulling ratification of the Constitution was a legal right not delegated to the central government. Simply put, the Constitution made no explicit mention of secession, ergo that right rested with individual states.

The States did ratify their secession through the popular vote through electoral conventions held in early 1860 and 1861. So there was a legal and parliamentary procedure that was followed that was consistent internally with due process.

In regards to 'peaceful means' - the Confederate States had indeed hoped that the North facing of a difficult 'end state': fighting the Confederacy and occupying a vast amount of territory would simply be happy to see the slaveholding states go their own separate way. It was Lincoln at the urging of Douglas who categorised the secession as an 'attempt to overthrow the United States government'.

Was this tantamount to a declaration of war? Or was the occupation of Fort Sumter a declaration by the Confederates? Was the refusal of Union troops to relinquish what Confederates saw as their land an act of war? Whilst slavery is a charged issue, when you remove it from the equation, it's quite easy to see Lincoln as the aggressor. He mustered a large army, and in the early days of the war seemed intent on taking the offensive (despite how disastrous this turned out to be).

In a modern context (say Israel or Sudan) we would definitely consider the Northerners the aggressors. The Confederates were by popular vote now an independent entity and Lincoln was fully prepared to use force to bring them back into the fold. In regard to the legal argument (re: Act of Congress) the issue is: Did the States need Congressional approval? Given that the Constitution never expressly forbade secession one would lean towards, well, no.

It's ultimately a matter of perspective, though. I think a lot of Americans see the war as justified because of Abolition. However, the debate at the time was more about the preservation of the Union and states rights versus federal ones with Abolition being an important issue but not necessarily always the central one.

Source: The West Point History of the (American) Civil War

Yes, North Carolina was attempting to secede on or around 1820. In fact a few states have attempted secession long before the Civil War.It was done by congressional bills drafted by the seceding states, and via diplomacy..the usual.

No, they did not use peaceful or legal means. Often the secession commissions used did not even fully represent the population of the state seceding. Southerners only started worrying about supposed legality after they lost the war and wanted to look better after the fact.

No, they did not. If they did, most likely they could get peaceful separation (considering that the Corwin Amendment passed Congress even without the votes of seven seceding states).

Instead, they recalled representatives from Congress, and demanded recognition from presidents (Buchanan and Lincoln), who did not have the constitutional power to change state legal status.

This power belongs to Congress, and the President must consider any state still in the Union, unless Congress recognized secession. And it is questionable that Congress could do this without the affected state(s) formally initiating this process. Also, it looks like voting a state out of the Union without this state's representatives participating in this vote is not constitutional - and seceding states representatives left Congress.

Seceding states could consider themselves out of the Union, and thus Union laws did not apply to them. However, if they wish legal recognition and peaceful separation, they better consider the way which does not require Union officials to break the laws.

First I will acknowledge it is difficult to write on this topic neutrally, even 150 years later, as the scar of the Civil War still runs through the country. I'll do my best to remain factual.

Did the Southern States make any attempt to secede from the Union, prior to 1861, through an act of Congress?

I cannot find any record of a serious attempt, no.

If not, what diplomatic/peaceful means were attempted?

The long running battle of States Rights and the idea of Nullification could be seen as this. At its head is the argument over Compact Theory, which has been rejected multiple times by the Supreme Court before and after the Civil War.

At the heart of the Nullification and Secession legal argument is Compact Theory, the idea that the US Federal Constitution is a compact between the states and any state can withdraw at any time. The foundations of the argument in favor are the Tenth Amendment which states that

The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.

The argument against is based on the idea that the Constitution is a document between the people and the Federal government, the states are not a party. This relies on the preamble which says "We the People" not "We the States".

We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America.

Furthermore, it is "We the People of the United States", acting as a body, not the people of each state deciding on their own. Various attempts by states to show local majority support for nullification relied on Compact Theory to be considered valid.

Compact Theory was ultimately shot down by the Supreme Court long before the Civil War. Chisholm v. Georgia (1793) upheld that Federal courts could hear disputes between states (immediately voided by the 11th amendment). Martin v. Hunter's Lessee (1816) ruled that states did not have the power to re-interpret Federal treaties. McCulloch v. Maryland (1819) upheld Federal authority to create a bank. All rejected arguments based on Compact Theory, but its use as a justification for nullification and secession persisted.

This came to a head in The Nullification Crisis of 1832. Had it not been resolved diplomatically, it could have lead to secession.

Mostly southern states, losing influence in the House of Representatives due to a declining share of the population, tried a new tactic. They argued they could selectively ignore Federal laws which their state felt were in violation of the Federal Constitution. This argument bypassed the Constitutional authority of the Supreme Court to make that decision. This all came to a head in 1832 over federal tariffs which the South did not like since they depended so much on cotton trade with Great Britain.

The rhetoric got hot and South Carolina passed legislation declaring the tariffs null and void within its borders on February 1st, 1833. Militias was raised to defend against Federal troops. They had a right to be afraid, the threat of Federal troops had been used against states to enforce Federal law before. Troops threatened New England states which refused to provide men for the War of 1812. Before that, the Whiskey Rebellion of 1791 was put down.

In the end, Congress negotiated a compromise tariff which satisfied both sides enough to back down. The particular issue was resolved, but the basic problem remained.

Similar negotiated issues which may have lead to secession include the Compromise of 1850 and the disastrous Kansas-Nebraska Act.

By the time 1861 rolled around the political and legal arguments had been gone over without resolution for decades.

What about various attempts by the southern states to poll their own people? While this may be peaceful, it is not diplomacy. As explained earlier in discussion Compact Theory, the Federal government rejected the idea that a state, or even its people, could decide alone to secede. Declaring you're going to ignore Federal decisions is not diplomacy, it is the end of diplomacy.

No, they didn't.

From their point of view there was now a hostile anti-South majority in Congress. Any attempt by themselves to do things to protect slavery through US Congressional action was doomed to failure. So there was no reason to bother trying.

The closest thing they had was allied Copperheads, Northern Democrats who felt the issue wasn't worth going to war over.