How do you find cheap rentals when your dog is on the breed restriction list?

Hi,

My husband and I are looking for a cheaper place to rent in Sacramento. We have two dogs. One Samoyed and one Malamute. Our Malamute is 80lbs (still growing) and less than a year old. She is on every single breed restriction list we have come across so far. We would love to find a cheaper house or maybe even a big apartment if necessary but having a Malamute makes it hard since they for some reason have a bad reputation when it comes to housing.

My question is therefore, does anyone know how you can rent with an Alaskan Malamute?

Please keep in mind that we have a very limited budget and buying a house is unfortunately not an option.