Get your GSD CGC certtified. The local GSD club can help you with that. (Canine Good Citizen Certification) Also, you can train him some service work and once a "therapy dog" he is considered a service dog and they should not be able to deny you rental. Most landlords are worried about aggressive dogs. GSD naturally are considered because of the type of work they do K9 Military etc .. Once they become educated on the temperment and how they are just loyal and protective they should reconsider. Make sure your dog is trained and not dog aggressive. Make sure they know that there property will be protected with this dog on the premise.
GSD lover