As far as I know, the answer is no. There were, for example, no other democracies in the Ancient Greek world, except for Athens. The vast majority of Ancient Greek states/regions, were governed by Tyrants, Monarchs or Oligarchs. Citizenship appears to have been a uniquely Athenian invention and a foreign concept to the vast majority of the Ancient Greek world-(both in Greece proper, as well as "Greater Greece" and "Anatolia"). Of course Athenian democracy, was far from perfect. Women could not vote, foreign residents had no hope of becoming citizens, slavery was widespread within Athens proper and in terms of numbers, citizens were in the minority of Athenian society though they wielded a great deal of power and influence. Few Athenians had the opportunity to join and speak within the Pnyx-(or Ancient Athenian Parliament).
The one figure who devoted a great deal of analysis to this question was Aristotle in his famed work, "The Politics". Aristotle analyzed the nature of various forms of government, including, Democracy-(or "Polity"). He discussed the Athenian Constitution and from what I remember, he also talked about the Carthaginian polity.
Carthage, was a great maritime empire that was located in the heart of North Africa and had dominated a sizable part of the Mediterranean sea region for centuries-(even during the period of Greek Mediterranean exploration and settlement, commonly known as, "Magna Grecia"). The Carthaginian empire had been the major imperial force within the Mediterranean region centuries before the Roman Empire. And while we tend to view Carthage as a major seafaring imperial power, according to Aristotle, the Carthaginians had their own unique version of a polity.
I don't have the exact chronology of Carthage's polity, though I know that Aristotle lived from 384 BC/BCE-322 BC/BCE and probably authored or lectured on "The Politics" during his years at The Athenian Lyceum-(around the 340's-320's BC/BCE). Most likely, the Carthaginian polity that he discussed, probably existed concurrently with Athens. Did the Carthaginian polity predate Pericles or Solon? I don't have the answer, though as I said before, it probably was contemporaneous with Athens.
I must admit that I am unaware of any "republics" in Ancient India. I was under the impression that most Indian states, in Ancient times, were ruled by Monarchs, though I would be interested in hearing more about Indian "republics" in Antiquity.