The main source for all researchers of Cheneys in New England is "The Cheney Genealogy" by Charles Henry Pope, 1898. However, it sounds like you are not far enough back, for most of the lines in TCG end about 1830-40, though some do go farther.
I'm not all that familiar with more modern sources. Quite possibly he died in the era when the State (or city) issued death certificates, which quite possibly would list his parents. It's also possible the newspaper of the town he lived in will have an obituary, and that newspaper is on microfilm in the town library.