I guess we're gonna have to rely on educated guesses from historians on this. It'd be interesting if we could compare the size of the population during the start of the Assyrian empire, the peak, and how it declined later on etc.
The book of Jonah described Nineveh as having "more than 120,000" people. Non-biblical sources stated that its population was close to 300,000 during Sennacherib?s reign (704?681 B.C.)
Not sure about the rest of the Assyrian nation, or Assyria as a whole.