I found the death notice for Adam Davis in the Falls City Globe-Journal of Apr. 26, 1879 (Saturday).
"DAVIS - In this city, at the residence of G. H. Gedultig, Friday morning April 25, 1879 Adam Davis, aged 58 years, 2 months, and 21 days.The funeral will take place this Saturday at ten o'clock.The remains will be buried in the Pearson Cemetery."
In the county cemetery listings compiled when the cemetery was walked by the local genealogical society, I also found the name of Nancy A. Davis.She died on the 12th of the month, but the month and year couldn't be read on her stone.
You mentioned in your post that Adam was a millwright.Do you know which mill he worked at?There was one in Jefferson Precinct (the Thacker Mill) where his widow was living in 1885.There were also two in nearby Falls City Precinct.
In the 1885 Nebraska State Census, Nancy was living with her son Richard (age 31) and daughter Mary A. Davis (age 21) on Richard's farm in Jefferson Precinct.According to this census, their father was born in Indiana, not Ohio or Ireland.