Sorry, but I believe many you are completely wrong when it comes to the "property owner's rights." The property owner is the owner of the property, when he leases it to someone, he leases the rights to that property. In other words, it is his house, but the tenant's home.
And in his own home, he has rights. You can't put in clauses that take away the tenant's right to privacy, their right to access, their rights to utilization, etc. The gun is NOT a damaging object, and it is the tenant's right to bring inanimate objects into the home as he sees fit.
Telling a tenant that he can't have a gun is like telling him he isn't allowed to bring in wood furniture because you're afraid of termites.