could any of the kingdoms at middle earth attack the southern continents?

[Inziladun]

Originally Posted by Nerwen

As for wars between the Haradrim and the Easterlings- well, we can't know anything about that, because the story is concerned with the west of Middle-earth. Again- you're asking for information that isn't there.

In the Unfinished Tales chapter Cirion and Eorl it is noted that the Wainriders of the East were "in conflict with the peoples of Khand and their neighbours further south". Whether that was an armed conflict is conjectural, though I think it likely there was combat between Men in the East and South at various times.

As for Gondor or any of the West invading other regions...well, if they could have, they would have. And the same goes for other peoples.