Recipe for rabbit stew, step 1. Catch rabbit!
I personally think the CSA even surviving with a POD any time after Lincoln's election is close to ASB. Assassinate Lincoln before he takes office? Fine...now we have Hannibal Hamlin instead. I think the Republicans would prosecute and win the Civil War. Pre-1860 PODs that result in a CSA must get there via a crisis similar to that of 1860 which will surely involve a strong movement analogous to the Republicans, otherwise the secessionist leaders would prefer to go on sock-puppeting the US federal government as they historically had at least since the age of Jackson. The secessionists were basically people who dominated the USA for all it was worth, and then tried to cut loose when evolving attitudes and demographics turned against them; you don't get a CSA without their opposition forming and getting strong first.
In order to discuss CSA post-ACW you need to first set the stage for the Union accepting a truce and letting the CSA be admitted to the community of recognized nations at all. Lots of TL's try this but they suffer from characteristic shortcomings as plausible TLs. Anyway everything depends on how the CSA survives, in what condition. Presumably they need strong foreign allies; will Britain, despite her many particular reasons to rejoice in setbacks for the USA, stand by the Confederacy? Will Napoleon III, especially considering his regime was loosely a British ally? Would it be in their interests to abet CSA industrialization, or would they much prefer the CSA to remain a dependent agricultural de facto colony? As noted above, what kind of society does the CSA have? Since slavery was the root reason for secession in the first place, anyone suggesting "they wise up and free the slaves" is indulging in the characteristic sloppiness of most Confederacy Survives TLs. They might wind up having to abolish slavery but something will have to twist the arms of the very same people who founded and ruled the thing.
IMHO the whole secession, and the general mentality of the people who led it, was concentrated idiocy and it imploded for good reasons. This leaves little room for rational contemplation of how it might fare!
I think it highly unlikely as I said that Northern leaders would just shrug and let them go--indeed many people did voice just such sentiments, but the question is if it came down to the point would a sufficient majority of them stick to it and face the consequences? Obviously there were arguments for doing just that since the consequences of refusing to allow the secession were quite severe.
Clearly if we are going to play this game, there are just a tremendous range of scenarios. Nerf the whole Civil War with someone other than Lincoln throwing in the towel immediately? That is a tremendously different situation than imagining the South wins some early battles so decisively the Union comes to terms after a year or two of civil war. Britain or France or both jump in as active allies? Highly improbable, especially despite Britains strong rivalries with America because of strong lower class sentiment against fighting the Union; this probably requires that Britain has some sort of strong reactionary regime. Certainly OTL American slavery was quite deplored even among the privileged conservatives who profited quite a lot from it. A POD might alter the whole tone and trajectory of Victoria's reign, perhaps by getting rid of her or just having something nasty happen in the 1840s like an abortive Chartist revolution leading to a highly reactionary regime; say the Chartists kill Victoria but then Wellington crushes them. Such a Britain might jump in, but we have to game out the consequences for British strength and power too. If Britain is so changed that the Empire is aggressively backing the CSA it is quite conceivable the net outcome is the two allies destroy the USA completely and the CSA leadership, not being quite total idiots, see to it that terms of creating a new puppet regime or three in the north (Britain hardly wants to see the CSA replace the USA after all, balkanization where they have a finger in both pies is their goal) and their general relations with Britain are not disadvantageous and favor their economic progress. I suspect that while slavery is inefficient in the industrial context, it would nevertheless be possible for slaves to be made to produce effective output and for a complex mixed slave/free industrial economy of some sorts to emerge from such a sweeping victory for the slaveocrats. You see, they have whips. And chains. I think there is more scope for CSA success along these lines if they double down on slavery than if they belatedly get on the enlightenment bandwagon. The whole 20th century might be a much starker conflict between property in a firmly and forthrightly reactionary framework brutally cracking down on the working people of all types everywhere, and equally brutal and desperate radicals, the whole concept of democracy might go by the board....which come to think of it makes this post of mine belong in another thread!
So I suppose it can be done but not in a pretty way.
The most likely way to have a CSA existing with a POD not long before 1860 is to have different Republicans who hand themselves an idiot ball or three and wind up fumbling the secession crisis, painting themselves into a political corner so that they first huff and puff and alienate Britain, maybe with some half-baked scheme to turn on Canada instead (I understand, perhaps misled by a not entirely reliable source, that Seward proposed such a volte-face) that blows up in their faces; they then ignominiously scramble for peace at all costs, surrender the border states and Washington DC to the Confederacy, and (if shots were fired in the north) other land to the British enlarging Canada to be, and get their act together later. This buys the Confederacy easy recognition and the support of European allies and allows them to face their internal problems as squarely as the nature of their leadership lets them. I think military necessity--everyone knows the Union is liable to go for round 2 sooner or later--might be adequately met, but this, along with the ideologically ramshackle nature of the CSA constitution that distilled the IMHO wrongheadedness of their whole project, will lock them into a quasi-dictatorship--which to be fair is ideologically consistent with slavery! On paper white CSA people are free, and considerable effective democracy would be in play, but in a fashion not conducive to systematic industrialization. A strong arms-oriented sector agreed to by consensus will to an extent serve as a springboard, but then the bad organization and warped social priorities of the victors will nerf it. Result, a heavy handed quasi-police state reliant on force and coercion, a highly disgruntled and alienated bunch of poor whites facing a strong but self-limiting quasi-aristocratic slaveocracy. The poor whites will not generally be what we would call progressive; systematic racism will be piled higher and deeper and turned against many people who passed as "white" OTL. Britain, if not herself transformed from OTL Victorian notions of progress and morality so as to become indifferent to or actively supportive of slavery, will maintain a facade of detachment contradicted by de facto alliance, and will be successful in steering the Confederacy in directions satisfactory to them, which probably means more stunting of CSA theoretical potentials. They might even short circuit the hothouse arms industry in favor of CSA being dependent on purchasing British made arms, even if the first generation of CSA leadership is shrewd enough to prevent immediate indirect rule.
Result--a dictatorial reactionary hellhole, a sort of right wing North Korea pariah state. Or perhaps it is most likely they survive at all in a situation where that type of setup is pretty much the norm everywhere, in Britain, in the paranoid and defensive Union, in Canada, in France; the whole liberal "project" implodes everywhere, much to the gratification of people like the Russian Tsars, Bismarck, the Hohenzollern king/Kaisers, etc.
But finally I repeat, I don't see this as highly probable. Most probably the CSA is reconquered by the Union more or less as OTL and things go on from there, in a range of possibilities depending on details.
