My son used my free ny statetax program. How can I buy another one?

What?   Do you have desktop download software?   If so, you can use that same software to prepare and e-file up to five federal returns and the state returns that correspond to them.   You do not have to buy anything else.

You just choose New Tax Return from the FILE menu at the top of your computer screen and prepare your own federal and NY return to e-file.  There is no fee to e-file a NY return.

If you are using online TurboTax, there are separate fees to prepare federal and state returns.

When you use online TurboTax software you get one return per fee.

Each return needs its own account and user ID.   If you use the same account and user ID for a second return, the second one overwrites the first return and it is lost forever.  

https://ttlc.intuit.com/community/using-turbotax/help/how-do-i-start-another-return-in-turbotax-online/00/25596