Edgar McDavitt
Born: 1809
Died: After 1876
Although I have no reputable source to site stating that there was ever a Mayor McDavitt, the name is listed in many places on the internet. These are just lists and they are always incomplete. During the early days of Memphis it was not uncommon for someone to serve as mayor for a brief time. James D. Davis in his "History of the City of Memphis" for instance sites that Elijah Coffey was briefly mayor although he is not commonly mentioned in that capacity.
The person being referred to as Mayor McDavitt is almost certain Edgar McDavitt, a banking and insurance tycoon from Kentucky. The McDavitt name had a long history in Kentucky and several members of the family relocated to Memphis. Of these only Edgar was ever active in politics, serving as alderman twice, once in 1851 and 53. That along with his standing as business partner with such notables as John Overton Jr. make Edgar McDavitt the obvious choice. Although neither Keating nor Davis mention him holding that office.
At various times McDavitt served as president of an Insurance company as well as two banks; the Bank of Commerce and the Planters Bank (this would later merge with the Union bank to form Union Planters).
In 1876 he helped to re-establish the "Old Folks Society", the earliest group formed for the preservation of the history of Southwest Tennessee. His wife was named Mary. The couple had four children. It is likely though not verified that Edgar McDavitt died between 1876 and 1880 as the 1880 census is the first to exclude his name.