Actually it depends on what you want to consider private ownership. If you are talking about local govt / municipalities owning heavier weapons then my answer is yes. Even in the colonial days, the general populace had small arms - but local authorities which were often converted into militia at need had heavier weapons. The British were marching to confiscate the heavier weapons when the local militias at Concord and Lexington impeded them to buy time for the cache to be moved to safety.

NYC is something of a modern example of this. NYC actually has quite a large stock of heavy weapons including anti aircraft missiles, armored vehicles, etc. Of course NYC is currently led by a fascist, who only wants people under his own authority to be armed and no one else. But many other cities and some Sheriffs actually have some sort of heavy weapons.

History has also shown that a populace with small arms, can in turn use small arms to acquire heavier weapons at need. So the general public carrying small arms during peacetime , with local authorities having the capability to stock heavier weapons is a decent paradigm that does not deny the natural right of humans to arm themselves but also does not encourage everyone to own a personal anti-tank or Stinger missile.

For who could be free when every other man's humour might domineer over him? - John Locke (2nd Treatise, sect 57)