Firstly, the goal is to create a POD that results in either a Confederate victory in the Civil War or, if you think you can manage it, the Confederacy being allowed to secede sans war. Secondly, what happens after the Confederacy becomes a recognized nation is immaterial at this point--so long as it survives long enough to be recognized, it doesn't matter if five minutes later it collapses, so long as said collapse isn't caused by a Union invasion.
Now then, what follows is my own rather vague thoughts on the issue--if you have an idea that doesn't fit into this outline, please share it anyway:
Right, the most plausible scenario from an American perspective (and please note that caveat) is one of early recognition for the South by Britain and/or France--basically they come in and save the Confederacy by threatening to spank the Union (a la TL-191). Problem is, from an European perspective, this doesn't make much sense. The American Civil War is at best a fight between two groups of slave-owning scumbags (until the Emancipation Proclamation, at which time any faint hope of Confederate recognition goes straight to Hell), and at worst, well, the USA is Britain's closest trading partner at the time.
My vague thought is this: what if US-European relations were considerably sourer? Say, the respective powers were bitter over the end of the War of 1812 and the animosity just grew from there. I don't really know why there'd be no opportunity to placate the animosity in that time frame, but as I said, this is just a vague idea.