Can the city by private act regulate hunting in the City? The answer is no.

You already have in your possession OAG Opinion 93-038, which opines that because of the comprehensive and pervasive state law regulating wildlife, including hunting, a municipality cannot by ordinance regulate hunting within its boundaries, or even prohibit the discharge of firearms, at least where the discharge is for the purpose of hunting. That opinion appears to be soundly-reasoned.

OAG 93-038 points to the proposition that ordinances cannot conflict with general laws on the same subject. The same proposition applies to conflicts between municipal charters and the general law, except where there is some reasonable basis for the departure from general law. [See Mayor of Alexandria v. Darman, 34 Tenn. 104 (1854); Hatcher v. State, 80 Tenn. 368 (1883); Williams v. Taxing District, 84 Tenn. 531 (1886); Grainger County v. State, 80 S.W. 750 (Tenn. 1903).; Knoxville’s Community Development Corp. v. Knox County, 665 S.W.2d 704 (Tenn. 1984); Shelby County Civil Service Merit Board v. Lively, 692 S.W.2d 15 (Tenn. 1985).] I can think of no reasonable basis for the departure from general law with respect to the City; its rationale for an exemption from the application of the general law governing hunting in Tennessee would not be distinguishable in any special way, from the rationale of any other city in Tennessee.
The solution to the problem with hunting in the City is a change in the general legislation governing hunting in Tennessee.