The easiest method would be as follows:
Step 1 - Give birth to the child.
Step 2 - Your mother can file a petition in Family Court seeking an award of custody of the child.
Step 3 - You go to Court with your mother when she receives notice to appear in connection with her petition, and you consent to the award of custody.
However, I highly recommend that you consult with an attorney before giving custody of your child to your mother (or any other third party) so you are well informed of the ramifications of doing so. Once you consent to give custody of your child away, it may prove very difficult in the future to get custody back if you change your mind. Good luck.
Mr. Rosen practices matrimonial and family law in Great, Neck, NY. His response here is not legal advice and does not create an attorney/client relationship. The response is in the form of legal education and is intended to provide general information about the matter in question. Many times the questioner may leave out details which would make the reply unsuitable. You are strongly advised to confer with an attorney in your own state to acquire more information suited to your particular circumstances.