Please excuse the very beginner level technical question here, but is there a way to create a Bitcoin private key with a simple consumer database app such as FileMaker Pro or Microsoft Access?

My guess is that there IS such a way, since both database apps include a "random number generator" function.

I suppose I just don't know where to find the information on:
1. What SPECIFIC criteria makes up a valid private key, including the checksum at the end of the key?
2. Once I have generated the private key, how do I translate that into the public key to distribute publicly to others?

My goal is to have my company's internal invoicing system (which prints out invoices on old-fashioned paper) automatically generate a brand new Bitcoin address (public key) on each printed invoice, so that clients can have the option of paying their invoices with Bitcoin.

Thanks in advance for any help or guidance that you can provide!