The ADA prohibits discrimination on the basis of disability in employment, state and local government programs, public accommodations, commercial facilities, transportation, and telecommunications.

Since Chow, Terrier, and Boxer are all on the list I have compiled of dogs to avoid/prohibit, I'm guessing it is likely such types of dogs are uncovered under my insurance policy.  

.- - - - - - - - - -PET AGREEMENT  (Addendum to Rental Agreement)The Month-To-Month Rental Agreement (the “Agreement”) dated_______________________ between __________________________________________________________________________, as Landlord and ________________________________________________________________________, as Tenant of real property located at _______________________________________________________, is hereby amended to include the following terms and conditions: The rental agreement specifically prohibits keeping pets and animals without Landlord permission; Tenant agrees to follow these terms and conditions in exchange for permission to keep a specific pet:Condition for keeping a pet:Tenant agrees to pay additional rent of _____________ per month for the privilege of keeping this pet.Tenant agrees to pay additional security deposit of ______________ for the privilege of keeping this pet.Name of pet: __________________________Description of pet: _______________________ (type, breed, color, age)Veterinarian: __________________________Emergency Caretaker: ____________________Tenant agrees to:1.Provide proper care for the pet in accordance with veterinary recommendations or ASPCA (American Society for the Prevention of Cruelty to Animals) guidelines.See www.aspca.org.2.Adhere to local ordinances, including leash, vaccination, and tag/licensing, requirements.3.Clean up after the pet and dispose of pet waste properly and quickly.4.Not to leave pet food or water outside the dwelling, as it could attract other animals.5.Not to leave the pet unattended for any unreasonable periods of time.6.Keep the pet from being noisy, aggressive, or from causing any annoyance or discomfort to others.7.Immediately remedy any complaints that arise from pet behavior.8.Immediately pay for any damage, loss, or expense caused to others by the pet.9.Provide pet with regular health care, to include inoculations as recommended by a veterinarian.10.Spay or neuter the pet when it becomes of age to do so.11.Arrange for an emergency caretaker for the pet.Tenant agrees to indemnify, hold harmless and defend Landlord against all liability, judgments, expenses (including attorney fees), or claims by third parties for any injury to any person or damage to property caused by Tenant’s pet.Landlord reserves the right to revoke permission to keep the pet should Tenant break this agreement or provide false or misleading information.

Of course we all have terms in the lease that prohibit general disruptive behavior. 

Nevertheless, it is definitely forbidden under the broader prohibition against discrimination on the basis of familial status.

Wait a minute, in one breath you say the lease prohibits pools, in the next you say you like the idea of having them take out liability insurance.

For example she could have a valid sublease unless your lease specifically prohibits that.

There is no "per se" prohibition against particular animals.

If you do allow it, just be sure to explicitly state on the lease and explain verbally that they are allowed "2 Guinea Pigs" only and that any other animals are prohibited without your prior written consent.

Any prohibition against asking prospective tenant for copy of current lease?