This is general information and not legal advice. No attorney-client relationship is formed. This is for educational purposes only.
It will help me answer your question if you could let me know when you say "NY paper," do you mean a NY newspaper where you are publishing notice to the unknown natural father?
If so, you would list him as "unknown natural father." If you have a way to contact Mother, you could go through the exercise of asking her for any information she may have about the father. It is unlikely to yield results. If the Child was placed with you by the State or an agency, you can ask the State or agency social worker what efforts s/he made to identify and locate the father.
If that is not what you mean, here are the usual efforts that must be made to seek permission to serve by publication:
-personal or mail service at last known address
-family and friends
-last known address
-last known employer
Obviously none of these will work to locate an unknown natural father, so you can point out to the court that such efforts would be fruitless, given the facts you laid out in your question.
If you are filing the guardianship yourself, you could ask at your Dover, Delaware family court for assistance in filling out the forms. Here is a link to Delaware Family Courts: http://courts.delaware.gov/family
At the bottom of the page you'll see "Information and Self-help," and within that section you'll find "Guardianship." You may already have accessed these forms and assistance, but if not, I hope this information is helpful.
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