The New York Genealogical and Biographical Society has an article in their
blog about substitutes for the Lost 1890 US census. Their article talks of
three substitutes for the census that was all but destroyed:

1890 Veterans Schedule this schedule survived for New York as well as other
states. It will include the name of the military person, rank, company,
regiment name, date of enlistment and discharge, length of service, post
office address, whether a disability occurred and additional remarks. It is
available on Ancestry.com a subscription service which is also available at
many public libraries and FamilySearch.org.
(https://www.familysearch.org/search/collection/1877095)

1890 New York City "Police" Census
In 1890 New York City consisted of Manhattan and western half of Bronx. The
Police Census is called such as the police were the enumerators.
FamilySearch.org released an index that covers the majority of the 1,008
books of which 894 survive today. The surviving books are available on
Family History Library microfilm and can be searched at:
https://www.familysearch.org/search/collection/2381996

1892 New York State Census
New York State took its own census every ten years between 1825 and 1925.
They skipped 1895 due to political and bureaucratic problems jumping to the
1892 census. Forty of the state's counties survived. Information including
name, age, gender, race, birthplace ( country), citizenship status and
occupation are all documented >from the census. To search the 1892 Census
see: https://www.familysearch.org/search/collection/1529100

Above are the three alternate choices for substituting the census. To read
the entire article may be found at:\
https://www.newyorkfamilyhistory.org/blog/new-york-state-substitutes-lost=-1890-census?utm_source=3Denews&utm_medium=3Demail&utm_campaign=3Denews+42
(MODERATOR: https://tinyurl.com/y233pk2z )

Jan Meisels Allen
Chairperson, IAJGS Public Records Access Monitoring Committee