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

[Inziladun]

Originally Posted by William Cloud Hicklin

At what period? At the height of the Kingdom, Gondor in fact did control large chunks of Rhun and Harad.

Though the sphere of Gondor's influence under King Hyarmendacil did extend to the Sea of Rhûn east and the River Harnen south, that was not an occupation or invasion. Gondor had defeated the Haradrim to the extent that the latter were compelled to pay homage to Gondor, temporarily. I think it's notable that in that case the sons of the kings of Harad lived in Gondor as hostages. That indicates that Gondor lacked the manpower for active occupation of the "conquered" territory.