Leaving asside the whole issue of having the CSA survive until the latter half of the 20th century, a dicey proposition at best, I just don't see Hockey making it in the south in any meaningfull way.
OTL the presence of teams and the existence of a, unfortunately still quite small, base of fans and players in the area was due to two facts:
I) The enthusiasm and renewed interest for Hockey in the US following the Miracle on Ice at Lake Placid in 1980.
II) The desire of building up the NHL for a solid television contract in the US and the assumption that some kind of solid overall geographic representation of most US regions to do so.
Since the Miracle on Ice was mainly won by players from the northernmost states in the US, who came from a longer tradition of Hockey made possible by the climates of the aforementionned states, I simply don't see the CSA being able to put a time together who might be able to make an ITTL version of it. If they're is some kind of Miracle on Ice equivalent it will be won by players from those same regions, which will be an american (as in ITTL-US) victory, not a confederate one. The spark of enthusiasm born of national pride that will came of it will simply not cross the border with the CSA.
Similarly, the tv networks of ITTL US are simply unlikely to care wheter the NHL, or its ITTL equivalent, has teams in the confederacy, leaving far less incentive for a risky expansion to the south.
Add that to the fact that the South is overwhelmingly likely to be considerably poorer then OTL, as well as that, to be frank, Hockey isn't doing all that well in the south as it is either and I just don't see an expansion of Hockey in the south.