Maybe once France has pulled out and is distracted by something else but for time being Mexico is untouchable right now. The only real path towards expansion is the Carribean and only really a few islands of which only Cuba would really be worth it.
Cuba has a similar economic model to the CSA, some cotton, but also valuable tobacco and sugar to be exported to the world. The CSA is very much going to be an export minded economy, so more that it can add the better. Tobacco and sugar are valuable staples the CSA would definitely
love to get their hands on to introduce to the global market. The sugar industry of the 19th century was an interesting one. In a small note, the US not having to worry about upsetting Southern sugar planters has already allowed Hawaii a free trade agreement on sugar in 1866 that OTL they were forever putting off, which has positive knock on effects for the Hawaiian economy and makes it just slightly less likely that the Americans on the islands will desire to annex them by force.
They aren't really, the US is going through a trying period but it's not on the precipice of collapse, and the CSA's "Three Good Presidents" doesn't necessarily mean that all subsequent leaders are terrible, they're just vastly overshadowed by their predecessors.
Call it the bad period for the US and what we can say is the good period for the CSA. The US has its "Era of Hard Feelings" after the war where everyone hates everyone contrasted with the "Era of Good Feelings" after the War of 1812.
There's not
exactly an "Era of Good Feelings" going on in the CSA right now, but since most of the political acrimony is directed at Davis personally and not any party apparatus, the potential for a national divide on political lines isn't quite there yet. That may change sooner than most think.