Dangerous breeds typically consist of: Doberman Pinscher, Pit Bull, Rottweiler, German Shepard and more but those are the common ones.
You can always charge a pet fee and increase the rent a small amount monthly as Nathan said. As for which breeds though some breeds have stereotypes of certain behaviors it is ultimately the animals environment and upbringing/training. Though you may want to check with your insurance company/agent as they can/have dropped people over certain breeds or they could require you get certain riders/add-ons with certain breeds. They could also exclude liability coverage for the animal(s) they deem a "dangerous breed" which that you do not want because then should something tragic happen you being the property owner would be liable out of pocket. Now I am not sure if to cover yourself in that scenario if you could in the lease somehow make the tenant get their own liability coverage for the animal you would need to check with an insurance agent and attorney on the legality of that. I am not even sure if insurance companies offer such policies to cover only the dog, and if they do if it is something that would release you from any liability of the animal should something happen.
It appears that most insurance companies will raise the rate 1% on "dangerous breeds".
My homeowners made me purchase a canine liability or threatened they would drop me due to the fact I have a pit bull even though he is big baby they consider him a "risk" and a "dangerous breed" though my lab they have no issues with.
No matter what you do though I would add in the lease that no pets are allowed to be on the property without prior written approval of management. That way you at least know what kinds of pets are on your property ahead of time, and it lowers the chance of putting you in a bad position of finding out a family got their children a cute puppy that they love and you come in and tell them the dog has to go. Trust me that will be hard, though its the right thing to do it will be hard.
I allow pets but require tenants to get written permission first and the animals approved to be on the property are listed in their file. I also have had MORE issues with cats over dogs, cats leave an odor and no matter what it seems every cat enjoys urinating in every room of the house, dogs for the most part go outside and the owners know it is their responsibility to clean up after their dogs even outside.