Hello. I wanted to share a few things that may help you. Do you know that when the "Pitbull Terrier" was created, years ago, they were bred to not bite humans. Yes, they can be animal aggressive. ALL Terrier breeds tend to be animal aggressive as they were bred to kill and control varments, like Rats (Rat Terrier) or Fox (Fox Terrier). The Pits were bred to not bite humans so back when they would fight the dogs, the handler could reach into the "Pit" and not be bitten.
What makes a dog "aggressive" is lack of socialization, lack of training and sometimes, poor breeding.
Any breed and any size dog can be aggressive. I personally am fearful of the ankle biters over the larger dogs as they are more high strung.
Rather then put restrictions based on BREED, make your determination based on the dog and the dog owner.
Is the dog well mannered, trained, full of energy or calm, does the dog owner provide the animal with enough exercise daily. There are many things to consider according to your own concerns, your property.
You can also put into your lease agreement that the dog needs to be muzzled while outside on the property.. things like that if it makes you feel better.
When you meet the dog for the first time, at the screening, did the dog bark at you, jump towards you, growl, listen to the owner's commands, make you feel uncomfortable? Say no to this dog, regardless of the breed. And if the dog is calm, well mannered, happy to see you.. this is a good potential tenant.
A very large portion of the population own dogs that have been put into the aggressive catagory. If all of the breed was aggressive like the media has said, all these people would not own them. There are bad dogs that are aggressive, but it is rarely a BREED thing, it is a bad dog owner.
Check out your local Animal Shelter and see what is the most common breed in there. You can ask them the most common reason dogs are surrendered, at the national level it is due to housing.