Pretty simple isn't it? Consult a lawyer in the State (even better yet the municipality) in which your property is located. Then you'll know exactly what you may or may not restrict in regards to firearms. The bottom line is that we should all run our businesses the way we see fit within the constraints of the law. Some people never allow pets, others do very well catering to pet owners. Some don't allow car maintenance in the driveway or on the premises, while others have tenants who won't move for 10 years because they love the extra deep two car garage that allows them to build a hot rod or restore Dad's old Buick.
I'm a gun owner and fierce defender of not only the Second Amendment, but all of them. I may not like your ability to restrict tenants from legally owning guns, but I also don't like the continued erosion of property owners rights in parts of our country (the Costa-Hawkins drama in CA is a good example). It's your property so do what you like (legally). If this issue is really important to you I would certainly suggest that you research the applicable laws in the markets that interest you.
Good luck with your investments, hope to see you post a "success story " or two in the future.
Cheers,
Mark