I have no idea if that city is easy to get a variance in, that would in all likelihood depend upon your new neighbors who are frequently notified when you request the variance.
I'd be more concerned with the setback requirements which if this is up to date according to
http://library7.municode.com/default-now/home.htm?infobase=19957&doc_action=whatsnew are:
Sec. 3-151. Restricted premises.
The keeping of agricultural animals shall be restricted to premises which conform to the following requirements:
(1) The premises must be at least one acre (43,560 square feet) in size;
(2) Fences on the premises must conform to City Code requirements. Agricultural animals may not be permitted to graze, forage, or otherwise roam nearer than 25 feet from any other adjoining property lines, including municipal property. This requirement may be waived for purposes of obtaining a permit from animal control to keep agricultural animals, provided that the adjoining property is currently zoned or used for keeping agricultural animals, and a notarized, undisputed written agreement between the property owners is submitted with the application for such permit;
(3) Barns, stables, corrals, sheds, hives, coops, pens, or other similar structure where agricultural animals may be housed, fed, confined, or where food is stored, must conform to City Code requirements and may not be located nearer than 150 feet from any residential dwelling, office building, school building, church, business, or other structure under separate ownership, which is intended for human habitation or use;
(4) There must be at least one-third acre of pasture area provided on the premises for each head of livestock, ostrich, buffalo, llama, emu, rhea, alpaca, Family Cervidae, or similar animal; and
(5) Up to five individual fowl per each one-fourth acre of land may be kept upon the premises. Fowl must be kept in a pen or other enclosure located at least 150 feet from any residential dwelling, office building, school building, church, business, or other structure under separate ownership which is intended for human habitation or use. Such pen or enclosure must provide at least 100 square feet of exercise area for each bird kept therein. In order to minimize the potential for noise nuisances to adjacent or nearby premises, roosters capable of crowing shall not be allowed to be kept within 1,500 feet of any residential dwelling, office building, school building, church, business, or other structure under separate ownership which is intended for human habitation or use.
