The 1790 and 1800 census records for the state of Kentucky no longer exist. However, there are still published tax records from that time available. They can fill in a lot of the missing census information for researchers.
The federal census for Kentucky from 1890 included a Union veterans and widows schedule. Records from that schedule for 65 of the counties in the state still exist. Several of the censuses for Kentucky have been indexed and published.
There are also published extracts available. The Kentucky Department for Libraries and Archives also has microfilmed federal census records on file. AISI has published several census records, but many of the census indexes for Kentucky that are readily available actually predate the AISI records.
Starting in 1888 Kentucky occasionally took public school censuses. Each county’s Board of Education or Board of Health may have some of those records available.