Okay, let me try this again.
Two major Tamil polities - Chola, and Pandyan - are mentioned in the written records left behind by Ashoka's empire.
The same two major Tamil polities (or polities ruled by Tamil dynasties of those names) are amply documented to have both been major Tamil empire in the early second millenium CE, with their history well documented for a number of centuries before that.
It appears accepted as plausible that the Chola and Pandyan of Ashoka's time are, in fact, directly connected with the medieval Chola and Pandyan. If they are so, then the Chola dynasy (fell in 1279 CE) can claim nearly 1600 years of existence, and the Pandyan (fell in 1618 CE) falls less than a century short of the full two millenia. That would put each of these two Tamil kingdoms, individually, in the run for the longest-lived kingdoms, ahead of Denmark and, in Pandyan's case, ahead of the most generous estimates for Japan that do not include the legendary emperors.
There's no combining of states, other than to state that the group, the Tamil monarchies, include states that, individually, are each the oldest or among the oldest monarchies in the world.