The following document from the Unified Court System discusses the methods of service of process in New York Courts:
The above constitutes general information only and should not be considered legal advice.
You can serve by mail pursuant to CPLR 312-a but the defendant does not have to accept it. If the defendant does not except it then you have to re-serve using a more traditional method and you can make a motion to have the defendant pay those costs. CPLR 312-a is very technical so be sure you follow it to a letter. It is probably better for a non-lawyer to have some serve the papers.
I am a former federal and State prosecutor and have been handling criminal defense and personal injury cases for over 17 years. The above answer, and any follow up comments or emails, is for informational purposes only and not meant as legal advice.