If you love a home and they are strict, consider offering a larger pet deposit. Put yourself in their shoes and see if you can find a creative agreement that satisfies their concerns. Letting them meet your well mannered 100lb dog may help too!
I'm a sales agent in San Diego - I don't work rentals but I thought this may help you in your search. Good luck!
Sarah Scott, Pacific Sotheby's International Realty
Basically landlords & management companies think bigger dogs can cause more damage than small dogs. When you meet for the rental, bring pictures of your dog with a "doggie resume" explaining why your pet is okay.
Best of luck,
Mark & Kari Shea
Shea Real Estate
National Association of Realtors
CA DRE License 01713506