It is harder and herder to find landlords who will accept pets. Unfortunately a small group of horrible pet owners ruin it for those of us who take the time to train our pets.
I ask all of my potential landlords to agree to allow pets before listing with me. So if you are in the market for another rental, give me a call and I can give you some options. However, any pet owner should know that they will have to be open to a serious security deposit. You get it back in the end (with interest) so whats the difference.