Did some research and found a transcription of the cemetery. Look like you are correct, from this, as to 1837..
https://www.cayugagenealogy.org/cem/cem155.htm
OWASCO RURAL CEMETERY
Burial Information for the period thru about the 1980s
For information on more recent burials thru early March 2007, click HERE
Although this cemetery is known as 'Owasco Rural Cemetery' and the Town of Owasco, NY
is located within Cayuga County NY, this cemetery is physically located just across the
county line in the Town of Skaneateles - Onondaga County NY (Cemetery #155)
This file is taken from a transcript done in purely chronological order. It’s been sorted by surname, and then chronologically within those names - obvious family groups have been recorded as shown. NOTE: * indicates cause of death known but not listed here - contact Cayuga County Historian’s office for more information. ** = Additional information from transcriber - personal knowledge.
Some E-Mail containing information about burials in this cemetery can be found at the bottom of this website.
This listing was obtained from The Secretary Record Books of Burials for the Owasco Rural Cemetery Association. Note: This list does NOT contain the date of death....The date cited is the "Date of Burial".
ENNIS
Daniel Dec 24, 1838 94
Eleanor, his wife Feb 14,1837 91