Taxes owed with a Amended return needs to be sent by check or pay on the IRS and/or State website. Choose to pay your taxes owed by check, that should get you through to e-file.
You can send in your payment with a payment voucher (1040-V), or for Federal you can go to the IRS website, to pay online.
https://www.irs.gov/payments
For State, you can check your State's website for payment options.
