My son is 24 and I have legally established paternity for him in Montana. He was born in NY. NJ collected child support all these years and also his father signed a support order and paid support for him until last year. My son is still on his health insurance until he is 26. My son's father now is claiming he is not his faterh.
I never had him put on the birth certificate because I thought having him declared the father in two states was enough. I want my son to have his father's name added to the birth certificate just in case. Can that be done?

Was the birth father adjudicated to be the father by the courts or was he just defaulted by the courts to be the father of the child? Also you will have to go with NY rules for adding him as the father to the birth certificate.

We had a court hearing and he was determined to be the father in Montana. He refused to take a blood test. MSorry not sure what adjudicated means. He then voluntarily signed an agreement to support our son, He paid over 300k in support and continues to have him on his health insurance. He just said in depositions in another case that he didn't have a son.
I am going to go to Vital Records on Monday. I have two certified copies of the court orders.

He was adjudicated. We had a court hearing that he was present at in Montana. He also signed an agreement in NJ that he acknowledged he was his father and would provide support.
My son is also on his health insurance.

Then you should contact the statistics dept of NY and ask them if the court records are good enough. From what your saying he did sign an Aknowlagement of Paternity. That is really all they need.

I want my son to have his father's name added to the birth certificate just in case.

In case of what? The son is an adult, so child support and custody would be moot.

As suggested, you can check with the New York vital statistics office and see if the BC can be changed at this late date. If the son wants his father's name he probably will have to apply (in whichever state he now resides) for a change of name. Whether the BC will be changed will depend upon the New York BC laws.