As
@Nightstorm86 astutely points out, there's still a mean little expansionist republic with a very imperial mindset amongst its worst political class that has its eyes set on the Caribbean. Not to mention European powers still sniffing around for advantage in the Americas. Spain may have just gotten some embarassing defeats in the Southern hemisphere and Caribbean in 1866-67, but that doesn't mean more established powers will not seek to get some advantage over the nations of the Americas while the US squabbles. Be careful who you take a loan from!
That said, Hawaii has a much more cosmopolitan and less "bombed by Japan" future ahead of it with the US now
very unlikely to annex it. There's some different politics coming in that direction!
Bullying their neighbours in the name of
slavery "free trade" is very much in the Confederacies interest. Unfortunately thanks to the war, they also have a very modern (for the 1860s and 1870s) and experienced navy to do it with! They also hold most of the Caribbean nations in contempt, and have big ideas about how they can (and should) gain an advantage over their weaker neighbours. They do need allies though, and the realists in Confederate politics are not stupid enough to believe that they can just do as they please, unlike the Fire Eaters. By and large they have some very mean ideas for the future.
Beating up the less than stable governments of Central America is well within their power. Outright annexation may be less than likely, but overt influence is a big possibility for the future.
There's a cabal that would like a bigger friend in Brazil too!