Corsairs use Adûnaic, the language of Númenor; you don't mean that, do you?
Could you toss a couple of examples of the Southron's tongue?
Nah, the Corsairs are essentially the descendants of Numenorean colonists as we as the descendants and followers of Castamir, I'm talking about the indigenous population of Harad. Tolkien gives us one word in their tongue: Mumakil. But there are several named Haradrim wb's/rt's throughout Gondor, such as Adîrjan, Luruyak, Vilosh, Keterang, Hokhir, Hamarsun, Darik, etc that are certainly not Adûnaic (as far as I can tell). Compiling this list, my first instinct is to say some kind of Indo-Iranian? But I'm not very well studied in that branch of the language tree.