My son was just born 2 weeks ago. How can I get him added to my 2019 tax return so I can get a stimulus check for him?

You don't add him to your 2019 return.  You will get the extra amount for him when you file your 2020 return next year.

You will receive any additional credit to which you were entitled when you file your 2020 taxes.  See question #27 here

https://www.irs.gov/coronavirus/economic-impact-payment-information-center

You can't.  If your child was born in 2020 you cannot add him to a 2019 tax return.  When you prepare your 2020 tax return in 2021--next year-- you can claim your child on that tax return.  The stimulus checks that people have received this year are really an advance for a credit you will be able to get on your tax return next year.  But congrats on your new little boy!