Working our way backwards: we know from the 1900 census that William Arthur McGuff, born Apr 1884 (actually 1883 per his gravestone) was living in Ridge Township, Fayette County, AL (which is just northwest of Tuscaloosa County), with his father William C McGuff, born Sep 1862 (at least according to this census). See https://www.familysearch.org/ark:/61903/1:1:M98J-YYH (the name was mistranscribed as McGriff here).
In 1880 in the same place there was a Mack McGuffee, age 17 (thus born ca. 1862/63) living with his brother James McGuffee (age 22, thus born ca. 1857/58) and James's family (see https://www.familysearch.org/ark:/61903/1:1:M4JJ-85Y). James was no longer present in 1900, but his son James N. (with last name now spelled McGuff) was living in the same precinct as William Chandler (see https://www.familysearch.org/ark:/61903/1:1:M98V-XSX). So I think it is safe to assume that the Mack McGuffie in the 1880 census is our William Chandler McGuff, and that he had an older brother James born 1857/58 (which would be soon after their parents' 1856 marriage). According to the 1880 census, both James and Chandler as well as both of their parents were born in Alabama. Thus, we should look for all of them in Alabama records, and with preference in the central-western section around Tuscaloosa.
Unfortunately, I have not found James (born ca. 1857/58) in either the 1860 or the 1870 census for Tuscaloosa or Fayette County.
There exist guardianship records for Tuscaloosa County for 1857-1868, which probably record who was appointed as guardian for the two boys; these have been microfilmed by the LDS but not digitized. Similarly, the land records (deeds) for Tuscaloosa County, which might reveal if the father Chandler ever owned land in Tuscaloosa, have also been microfilmed but not digitized.