As there are no paternal rights to sever (presuming this was done properly, through a sperm bank), you and she can hire an adoption attorney and have them handle the whole thing. Your parental rights can be severed (that is what your post implied was wanted) at the same time that the adoption is done.
Here is a summary of NY adoption statutes:
New York Adoption Statute Summary
New York Domestic Relations Law Sections 109 to 117 and New York Social Services Law 372 to 373 (1997)
Who Can Adopt?
Any adult unmarried person or an adult husband and wife jointly may adopt. Any adult married person who has been living separate and apart from his/her spouse for 3 years as long as the person being adopted is not deemed the child or stepchild of the nonadopting spouse. A minor spouse may adopt his or her own, or the other spouse's child which was born either in or out of wedlock. In an agency adoption, the judge or surrogate when practicable must give custody only to persons of the same religious faith as that of the adoptive child.
Who Can Be Adopted?
Any person can be adopted.
Consent to Adoption
Consent to the adoption is required of the following parties:
1. both natural parents of a child conceived or born in wedlock;
2. the mother of a child born out of wedlock;
3. the adoptee who is over 14 years of age, unless the judge waives this consent;
4. the person or agency having custody of the child;
5. the father of a child born out of wedlock, if he has maintained substantial and continuous or repeated contact with the child as demonstrated by
o payment of child support and
o visitation of the child at least monthly when permitted and financially able to do so, or regular communication with the child or agency having custody of the child when permitted and financially able to do so; and
6. the father of a child born out of wedlock who is under 6 months of age at the time he is placed for adoption, who has lived continuously with the child or the child's mother for 6 months before the adoption and who held himself out to be the father.
Consent is not required of a parent when
1. the parent evinces an intent to forego parental rights by failing, for a period of 6 months, to visit and communicate with the child;
2. the parent has given the child up to a child-placing agency;
3. a guardian has been appointed for the child;
4. the parent is mentally ill or mentally retarded and is unable to, now or in the future, provide proper care to the child; or
5. the parent has executed an instrument denying paternity or consenting to the other parent's surrender of the child.
In the case of a private placement adoption, once a judge has acknowledged consent to the adoption it is irrevocable. In accepting such consent the court must advise the parents of their right to counsel and supportive counseling. If the consent has not been executed or acknowledged before a judge it may be revoked within 45 days after its execution.
Putative Father's Registry The Department shall establish a putative father registry of: any person adjudicated by a court to be the father, any person who has filed with the registry a
notice of intent to claim paternity, any person who has filed with the registry an acknowledgment of paternity. When a father has filed with the putative father registry, he is entitled to notice of the adoption.
Confidentiality
All records in adoption proceedings are to be sealed and secret. No information shall be released except upon a court order for good cause and upon due notice to the adoptive parents. No mention of the fact that the child was born out of wedlock shall appear in the record. The State also maintains an adoption registry where, if the biological parent and the adoptee consent, identifying information may be released to each of them about the other party. In addition, nonidentifying information about the biological parents may be released to the adoptee.
Provisions prohibiting the surname of a child from appearing in the papers and disclosure of the surname of child to adoptive parents, and requiring a separate application for issuance of a certified copy of an order of adoption prior to the sealing of the papers, and the filing of a verified schedule, shall not apply to private placement adoption.
The adoptive parents shall be provided with extensive information regarding the child's medical history and heritage of the birth parents, such as their nationality, ethnicity and race (including drugs taken during pregnancy and hereditary conditions), and hobbies and talents.
Permissible Fees
In private placement adoptions, the adoptive parents must present a statement to the court which describes all fees, compensation, and expenses paid in connection with the adoption. The attorney representing the adoptive parents must also present an affidavit describing all fees and compensation received.
Place of Adoption Hearing
The adoption hearing may be take place in the county where the adoptive parent lives, or where the agency that has custody is located.
Authority To Place Child
Either a public child-placing agency or a private child-placing agency may place a child for adoption. In a private placement adoption, prior to the transfer of physical custody of the adoptee, the adoption parents must be certified as qualified parents by the court. In private placement adoption, a parent having custody of a child whose adoption is sought by a named stepfather or mother need only consent that his or her child be adopted.
Relative Adoption
There are no provisions in the law regarding relative adoptions.