You can use your private army to gain currency and other assets by stealing them from other entities. Governments typically don’t like this but if you’re a big enough force they will negotiate.

Maintaining a large private army would be expensive and time consuming.

So is maintaining a large workforce and infrastructure, but they do that as a matter of course. And already, there are corporations with operating budgets larger than some countries. That's only going to become more the case with time.

What stops another corporation with a private army from coming in and robbing them of everything they have?

The same things that generally stop countries from doing it to each other - insufficient forces and/or unacceptable losses and/or a preference for stability and/or established alliances and/or any of countless other considerations.

This isn't rocket science. Realpolitik is a fairly straightforward thing.

Where is the corporation getting their funding from?

From the sale of goods and/or services.

Duh.

Someone’s got to be paying them.

Yes. Consumers of whatever goods and/or services they provide.

Duh.

So, they are using a sovereign currency created by a government using a central banking system chartered with the government.

Or more likely not.

Here's just one quick idea - accept local currency with a handling fee sufficient to cover any potential losses on exchange (which are unlikely, since at that point their currency will likely be harder than about any government's), and advertise a discount for the use of their private currency, accompanied by the offer of free and automatic currency exchange with an account at the corporate bank.

So you promote your currency, avoid the hassle of dealing with competing currencies and gain new bank accounts, all at the same time.

And that's just one idea, off the top of my head.