Confirm that you are eligible. Then, confirm the institution is truly eligible and contact the institution for their EIN.
I recommend reviewing the 2020 Instructions for Form IT-272 Claim for College Tuition Credit to confirm your eligibility. It is separate from filing for the federal education deduction or credit.
The additional New York Deduction or Credit only applies to full-year resident persons pursuing an undergraduate degree, not claimed as a dependent. Qualifying expenses will not include room and board or fees for course related books, supplies, etc.
See Publication 970, Tax Benefits for Education, page 13 and 14 reviews the definition of qualifying educational institution:
Eligible educational institution. An eligible educational institution is generally any accredited public, nonprofit, or proprietary (privately owned profit-making) college, university, vocational school, or other postsecondary educational institution.
Also, the institution must be eligible to participate in a student aid program administered by the U.S. Department of Education. Virtually all accredited postsecondary institutions meet this definition. An eligible educational institution also includes certain educational institutions located outside the United States that are eligible to participate in a student aid program administered by the U.S. Department of Education.
