Is there no way to remove a father's name off a birth certificate in New York State after 60 days when he is not the biological father?

First, it is not a good idea to piggyback your question on another thread. To avoid confusion your question has been moved to its own thread.

Sure there is a way, you go to court and ask that the birth certificate be amended.

If you are asking whether it can be done without a court involved, the answer is no.

Social Services Law §111-k(2)(a) mentions the issue of disestablishment. It states that either signatory (either parent) can file a court action to vacate the acknowledgment, within 60 days of signing the acknowledgment. Also, after 60 days, either parent can challenge the acknowledgment in court action based on fraud, duress or material mistake of fact.