I've found some information, but I believe the first quoted two passages may not apply, because they unfortunately apply strictly to urban areas. You may be able to make a case off of the 1935 nuisance law, the final quoted passage, though...
Good luck, usually this information is pretty easy to find but Yakima's site isn't very clear.
Chapter 15.09 SPECIAL DEVELOPMENT STANDARDS
15.09.070 Special requirements for animal husbandry.
A. Purpose. The purpose of this section is to assure that the raising of domesticated farm animals within the urban area is compatible with adjoining residential uses and the intent and character of the district they are located in.
B. Minimum Lot Size. The minimum lot size for animal husbandry within the Yakima urban area is one-half acre. A lot at least one-half acre in size shall be deemed to meet this requirement even though a portion of the lot may be used for a single-family dwelling.
C. Project Review. Animal husbandry operations, which would create noise and odors, attract insects or rodents or are otherwise incompatible with surrounding residential uses or the intent of the zoning district, may be conditioned or denied by the reviewing official in accordance with the provisions of this section.
D. Minimum Setback.
1. No portion of any structure used to house a domesticated farm animal shall be located within one hundred feet of any residence other than a dwelling on the same lot; and
2. No portion of any structure used to house a domestic farm animal shall be located within ten feet of a residence where the residence and domestic farm animal structure are located upon the same lot/tax parcel.
E. Maximum Number of Animals. The maximum number of animals that may be kept on the site at any time of the year shall be the number of animals that can be sustained by the pasture on which they are kept as their primary source of food, except during the winter months. The burden of proving that the pasture can sustain the number of animals in question shall be on the applicant.
F. Fencing. Fencing adequate to contain the animals shall be provided and maintained. (Ord. 2011-52 § 8, 2011: Ord. 2010-16 § 13 (part), 2010: Ord. 2009-09 § 1 (part), 2009: Ord. 2008-46 § 1 (part), 2008: Ord. 93-81 § 43, 1993; Ord. 3106 § 21, 1988. Formerly 15.09.090).
Chapter 15.04 PERMITTED LAND USES
15.04.060 Accessory uses.
D. Pets. The keeping of pets is permitted as an accessory use; provided, that in residential districts they are subject to the following restrictions (see definitions of “kennel” and “animal husbandry”):
1. They are domesticated animals kept for pleasure or as a hobby rather than utility, including, but not limited to, fish; birds; dogs, four; cats, six; hen chickens (no roosters), fewer than five; and rabbits, fewer than five;
2. Their presence does not create undue noise or odors such as would create a nuisance or diminish the residential nature of the neighborhood;
3. Such animals are properly fed, watered and kept in a humane manner;
4. Any chicken coops, chicken tractors, or rabbit hutches shall be set back ten or more feet from any residence or property line, and five feet from other structures including decks;
5. Hen houses, coops, hutches, and chicken tractors shall be restricted to the backyard area of a residential lot;
6. For chickens and rabbits, adequate fencing shall be installed to contain the animals within the backyard;
7. The other provisions of the YMC for animals are followed.
Chapter 6.56 NUISANCES
6.56.060 Offensive confinement of animals.
The keeping, using or maintaining of any pen, stable, lot, place or premises in which any hog, cattle or fowl may be confined or kept, in such manner as to be nauseous, foul or offensive, or from any cause to be an annoyance to any community, family or person is declared to be a nuisance. (Ord. B-86 § 1(f), 1935).