We know that Orcs like to reside in mountains, which there is a range of in Rhun. I don't know of any mountains in Harad.
But is there any indication that orcs resided in Rhun or Harad or both?
According to the Ambarkanta maps (published in History of Middle-earth 4) there should be at least one chain of mountains in Harad: the Grey Mountains (not to be confused with the other Grey Mountains north of Mirkwood), running along the west coast from north to south.
There is however no evidence that I am aware of for Orcs living in either Rhun or Harad.
A hypothetical case can be made against Orcs living there, which is that Sauron had successfully corrupted most Men from these areas, and so he would have had little need for Orcs.
In the east and south well nigh all Men were under his dominion, and they grew strong in those days and built many towns and walls of stone, and they were numerous and fierce in war and aimed with iron. To them Sauron was both king and god; and they feared him exceedingly, for he surrounded his abode with fire.
(Of the Rings of Power and the Third Age)