Legal Question in Family Law in Oregon

NO, you cannot "sign the birth certificate." Even though you will be caring for the baby, the baby is not your child until and unless a formal Judgment of Adoption is signed by a judge and filed with the court records of the having legal jurisdiction over the adoption matter.

Also, suggest you talk to a lawyer about alternatives to adoption. Interfamily adoptions often result in many unanticipated problems. Unlike traditional adoptions, which change both the legal as well as practical aspects of the child-parent relationship, interfamily adoptions usually change only the legal relationship. In other words, despite the adoption, your niece and nephew will forever view the child as being THEIR child, not yours. And you will be viewed simply a "caretakers," not "real" parents. And many, many problems will arise in future years.