What counts as a "clear majority?" 50% plus one?
There was . . . let's see, one state where the slave population exceeded the free population: South Carolina (301,302 free versus 402,406 slave). I don't have time to go digging into an age demographic breakdown, but let us assume it holds true for the voting age male population. Of course, South Carolina did not put secession to a plebiscatary vote: it was adopted by a special convention called for the purpose.
There were a few other states where the opposition to secession was strong enough that a vote by African-Americans, if it were possible, could probably give that opposition a majority. That assumes that all, or virtually, *would* vote thusly, which might be an assumption that needs to be unpacked with some care.
But I think that we have concede the possibility that, even with universal suffrage to all adult males over 21 (the most common cutoff age in 1860), and putting the question to a popular referendum, it is quite possible that we would have several southern states still finding a majority for secession.
Of course, note that we are not talking about another important non-enfranchised population cohort: adult women, of any race. Not that they had the vote in any northern states either...
Well of course there were also white unionist minorities, often very significant ones even if many people who opposed seccession initially fought for the slavers later, I think they're enough that when you add in slaves there wouldn't have been even a bare majority for secession anywhere.
As far as peace later on, as I've said before in this thread often the best hope for black freedom after the war would be moving west with Federal support. There were a lot of black cowboys etc. historically just increase that enough to get a lot of Western black majority communities due to low population bases.
Of course that'd fuck over Native Americans horribly and you'd probably have a lot of black majoritiy areas ignored for development purposes but it might be the easiest way to get a lot of ex-slaves out from under the boot of racism.