in the other hand, Vatican only straight on ban slavery in early 20th Century
The Catholic Church is small enough in the south that I don't think their opinions on anything will matter.
Pius IX was on a personal level a supporter of the CSA, and on some level a supporter of the institution of slavery (provided that the slave's liberty was "justly" deprived--that is, it is right and just to enslave a criminal or to have an indentured servant, whereas slavery from birth is unjust). But Leo XIII in no uncertain terms condemned the institution in the 1880s, after Brazil abolished it. (http://www.vatican.va/holy_father/l...ts/hf_l-xiii_enc_05051888_in-plurimis_en.html).
These factors in mind, I think the Church would urge Confederate Catholics to free their slaves and perhaps set up ministries aimed at buying and freeing slaves held by Protestants. And I don't think Richmond would do much to prevent Catholic priests from spreading this teaching.
On the other hand if they do this the CSA is gonna suppress the church. There's no way they'd allow a major abolitionist group to operate freely in their territory.
I think they'd get quite a bit of sympathy, though. States like Tennessee or and North Carolina were dominated by poor farmers without much love for their plantation-owning cousins across the southern border. And in rural areas, the Church was often a major source of education--Jeff Davis got his education from the Dominicans, and in fact attempted to convert in his youth before he left school and lost interest. He and other Confederates with such positive histories with the Church wouldn't be quick to form a secret police force. Besides, wasn't freedom of speech a feature of state constitutions? So long as they're not actually agitating for the criminalization of slavery, what law would they be breaking by buying and freeing slaves?