While the 1890 Population Schedule did burn, the 1890 Census Veterans' Schedule (mostly Civil War vets) survives for the States beginning with the last half of the alphabet.
Isn't there also an 1892 NY State Census?
There's a database of late 19th-century Russian immigrants on www.familysearch.org
. I only noticed because I was disappointed it did not go up to the time period my husband's paternal grandfather immigrated as result of the 1905 pogrom.
Of course if they came from the part of Ukraine that was at one time in Prussia and subsequently Poland, that might not be very helpful. People who can navigate these 19th-century boundary/invasion/kingdom issues deserve prizes.
At least try a global search on that site, you might come up with some jewels. The site does not tell you up front that you can use wild cards in name searches: * = any number of letters, ? = one character. So to search for Denisovich that has typical spelling variants, try D?n?s*i*; this will give you Polish-style character variations such as ...wicz.
Also don't fail to look at the browse-only NY estate ("probate") records on that site, you might espy a record book for the right time and County (you do know what County they died in?) and strike riches. The records books of various types often have name-indexes in the front, and there is often an estate/docket index, so it's not all (or even mostly) blind browsing.