Go to the
www.irs.gov website and get the forms and instructions for 8839. You will be able to apply for credit for each eligible child whether it was successful or not. You can claim up to $10,000 for each child.($9000 for one, $10,000 for the second) Just make sure you have your supporting documentation.
To get the adoption taxpayer number you will need Form W-7A.
Like the one of the previous posts stated...make sure you run it by a tax professional.