I have found your municipal codes online and they are very strict, but do not necessarily preclude you from ever keeping such animals as they have specific procedures in place for requesting variances for animals. Here is the section on how to apply for a variance. They have it all laid out for you. Your best bet is to know this and follow it to the letter:
5-18.4 Application for Waiver; Notice.
An owner desirous of owning and maintaining a non-domestic prohibited animal as provided for herein shall have the right to make application to the Mayor and Council of the Borough for a waiver under this section. The application for a hearing before the Mayor and Council must be submitted not less than ten (10) days prior to a regularly scheduled meeting, with notice published in the official newspaper of the Borough of Fair Haven not less than ten (10) days prior to said meeting, and giving written notice to all property owners within two hundred (200) feet of the applicant's property. The applicant shall obtain a certified list of all property owners within two hundred (200) feet of his/her property from the Borough of Fair Haven's Tax Assessor's office.
a. Type of Notice. Notice must be made to all property owners within two hundred (200) feet of the applicant's property by regular and certified mail, return receipt requested, with proof of service being presented to the Mayor and Council at the time of the hearing with an affidavit setting forth that the mailing has been made to the appropriate property owners.
b. Form of Notice. The notice shall set forth the following:
1. Name and address of the applicant.
2. The address and lot and block number of the household or dwelling unit for which the applicant intends to harbor the non-domestic animal.
3. The nature of the waiver requested, setting forth the number and identity of the proposed non-domestic animal.
4. The date, time and place of the hearing before the Mayor and Council.
c. Consideration for Granting of Waiver, Burden of Proof and Vote. By majority vote of quorum of the Borough Council, the Mayor and Council may grant or deny an application for a request for a waiver based upon a preponderance of evidence that the applicant has demonstrated good cause for the granting of such waiver. In examining whether or not a waiver should be granted, the following shall be considered:
1. The size of the property of the applicant where the non-domestic animal(s) are intended to be kept.
2. The distance between the location of where the non-domestic animal is intended to be kept on the applicant's property and the physical location of an adjacent property owner's home or dwelling unit.
3. Whether the applicant's property is fenced so as to shield the non-domestic animals from the sight of the surrounding property owners.
4. Whether the non-domestic animals are kept in the applicant's home or remain primarily outside of the applicant's home.
5. The proposed non-domestic animal and its size.
6. The prior history of complaints filed against the applicant for violation of this section, or previous ordinances pertaining to animal control.
7. The zoning district of the applicant's property,
8. Whether the non-domestic animals serves some purpose other than the desire to have a non-domestic animal as a pet.
9. For other such reasons as the Mayor and Council may feel appropriate to consider according in the case, facts and circumstances presented at the time the application is heard.
d. State Number of Non-Domestic Animals. Should the applicant's request for a waiver be granted, the Mayor and Council shall set the number of proposed non-domestic animals permitted.
e. Revocation of Waiver. A waiver granted by the Mayor and Council may be revoked upon proper application made by a Borough official, member of the Borough Police Department or an individual by making applications to the Mayor and Council at least ten (10) days proper to a Council meeting and by serving notice upon the owner by regular and certified mail, return receipt requested, of the application for revocation of the waiver. The notice shall also include a factual basis for the requested revocation. A hearing shall then be held by the Council on the application for revocation. The Mayor and Council will evaluate the application for revocation of waiver based upon the same criteria previously set forth herein under this section.
f. Vacancies. All non-domestic animals as authorized by a waiver shall be vaccinated against rabies and any other disease as required by a licensed veterinarian and all vaccines shall be done in accordance with the following:
1. Vaccination shall be performed by a veterinarian licensed to practice in the State of New Jersey. The vaccine used shall be from a manufacturer licensed by the Bureau of Animal Husbandry of the United States Department of Agriculture or such other agency as shall be approved by the State Department of Health. The dosage shall be as recommended by the manufacturer. All animals shall be revaccinated before the expiration of the period of time for which the vaccine used is known to be effective.
2. No waiver shall be granted until the certificate indicating that the animal has been vaccinated or otherwise inoculated has been presented to the Borough Clerk. The certificate shall be submitted with the request for a waiver application but no later than the hearing date schedule for the waiver application hearing.
(Ord. No. 2008-19)
5-18.5 Limitations on Granting of Waiver/Permit.
The granting of a waiver and permit hereunder shall in no way authorize the creation of a nuisance or the maintenance of an obnoxious condition and shall in no way regulate or prevent the passing of future ordinances concerning the prohibition of or the limitation upon the keeping of non-domestic animals. (Ord. No. 2008-19)
5-18.6 Term of Permit; Expiration; Fee.
Any permit granted after obtaining a waiver, shall be valid for a period of one (1) year from the date it is issued. A permit must be obtained on annual basis. The permit fee shall be twenty-five ($25.00) dollars. (Ord. No. 2008-19)
5-18.7 Building, Feeding and Operational Requirements.
Any person having obtained a waiver as set forth herein shall comply with the following provisions:
a. The storage of any such non-domestic animal shall be such as to preclude odors and sounds therefrom from interfering with the comfortable enjoyment of life and property on neighboring premises.
b. Building, food storage bins, appliances, equipment, feeding areas and other facilities on the premises which might provide food or shelter are to be constructed and maintained in such a fashion as to permit proper cleansing.
c. The water supply shall be adequate for proper sanitation.
d. Water or other liquids to which mosquitoes may have access shall be properly treated to prevent their breeding.
e. Rodents to insects hazardous to public health shall be controlled so that they do not exist or reproduce therein or thereon.
f. Adequate equipment shall be available to maintain all yards, enclosures or premises in which such non-domestic animals shall be kept, raised or maintained in a sanitary condition at all times
(Ord. No. 2008-19)
5-18.8 Fencing.
The area wherein the non-domestic animals are kept, except where they are housed in closed buildings, shall be completely fenced with a sturdy, well constructed closely woven wire fence or other equally effective fence so as to prevent trespassing on adjoining property. (Ord. No. 2008-19)
5-18.9 Violations and Penalties.
A person guilty of violating the provisions of this section shall be subject to a fine in an amount not to exceed one hundred ($100.00) dollars for the first offense and no more than five hundred ($500.00) dollars for all subsequent offenses. (Ord. No. 2008-19)