Adoption expenses are deductible in the earlier of the year the adoption becomes final, or the year after they are paid. For a failed adoption, that would be the year after they are paid. Consequently, if you pay them in 2016 they would be eligible for credit in 2017 (which, at the earliest, you would claim on your 2017 return filed in January 2018..
(An exception is for a foreign adoption, where for a failed adoption, they are not eligible for a credit at any time.)
