I'm afraid a Presidential victory is out of the question, without some sort of truly radical POD; the good majority of the Know-Nothings weren't actual committed abolitionists anyway. Sure, some did indeed jump on to that bandwagon(namely, quite a few of the Northerners) after all, abolitionism was rapidly becoming more and more of a popular subject of debate in the 1850s up North......but the Know-Nothings' real forte, first and foremost, was that of anti-Catholicism and anti-immigrant sentiment in general. The only major reason they fell apart, really, is because they were divided on slavery; there were a fair number of Southerners in the movement before it died as well, and quite a few of them supported slavery, or at least did not oppose the institution.
There is one surefire way to save the party for another decade or so.....but it involves jettisoning the abolitionists. Yes, you read this right: to save the Know-Nothing Party, the abolitionists are going to have to be shoved out(and into the Republican Party). Once that happens, though, they stand a much better chance of keeping their support alive down South and could, under the right circumstances, even become a plurality or even majority Southern-supported significant party(do remember that the South was fairly anti-immigrant, particularly anti-Catholic in many places, even before the Civil War; it's part of the reason why the Klan became so popular). It might involve delaying the Civil War for a decade or so, but it could still be pulled off even without that.