As you have discovered, it is, in my own experience with helping my clients, difficult to find rentals that will take pets, not to mention large or two or more pets. I have a dog myself, so I understand how important our pets are as they are our family.
I think the only way you can find out is to call each owner/agent personally and plead your case. You might also be able to negotiate it by offering larger deposit and/or just a bit higher rent and see if you can find some owners that will allow pets with some incentive from you.
Hope this helps!
all the best,
Bradley Real Estate