Private adoptions can be scary from their perspective should you change your mind, but they are very common. You do not have to get an agency involved. You may want to seek a lawyer that is not a general practice or even a family lawyer, but someone who specializes in adoptions.
Here is a directory to find an adoption lawyer:
http://directory.adoption.com/
In a private adoption you will just release your rights to the adoptive parents and not to and agency. There is no reason to get a middle man involved, if both you and the parents are fine with the terms.
http://ffpa.org/faq.php4



