Here's what I'm finding on Ancestry:
1870 Census: Joseph and Cordelia were still married and living in Lewisburg North Ward, Union, Pennsylvania, United States. William N. was 8 years old; Cynthia Mary was 2 years old.
1880 Census: Joseph is divorced and living in Buffalo, Union, Pennsylvania, United States. He appears to be boarding with an older gentleman, George Darr.
Cordelia is still listed as married, living in Southport, Chemung, New York with her parents, two of her siblings, and William and Cynthia.
An 1894 U. S. City Directory appears to show Cordelia living in Elmira, New York. She is listed as a widow of Joseph. No mention of Cynthia, but William N. appears on the next page at the same address.
HOWEVER, the 1900 U. S. Census shows Joseph still alive and well (and divorced, living alone) in Buffalo, Pennsylvania.
The same census shows Cordelia married to Charles Bulkley and living in Osceola borough, Tioga, Pennsylvania.
Joseph MAY have died in 1902. Other ancestry trees show this as his death date, but no evidence. The only proof I have is from FindAGrave: a Joseph B. Davis, who is buried in Lewisburg Cemetery, Union county, PA, b. 25 December 1822, d. 14 May 1902.
Hope this is helpful for you! According to my Ancestry tree, Cordelia is my 3rd cousin, 5 times removed. My common ancestor with her is Richard Tozer (1675 - 1729), my 7th-great-grandfather and grandson of Richard "the Immigrant" Tozer. So this helped me extend a neglected branch of my tree as well :)