If you are looking for rental housing that allows pets, check these sites out:

 http://www.myapartmentmap.com/pet_friendly/
http://apartmentlist.com/ca/los-angeles
http://www.rent.com/pet-friendly-apartments
https://www.zumper.com
http://hotpads.com/search/pet-friendly-apartments
http://www.zillow.com
https://www.forrent.com/library/renters-guide-pet-owning

and here is a pet friendly housing guide to help prospective renters: https://www.zumper.com/rental-guides/how-to-rent-pet-friendly-apartments/