First I will admit to being a gun owner and an active NRA member, so there.
While not a lawyer, it would seem to me the critical discussion is the business owners right to allow the possession of guns on their property. Even in Texas there is a special provision in the law for businesses to request the concealed carry permit holders to not carry on their premise. And I think rental property would be considered a business property. So if you advise tenants of the "no gun policy" prior to signing a lease, it would follow possession of firearms would be a violation of the lease agreement. All of this would have to be clear at the onset of the lease, not after the fact.
Now as a little side note, when first married along time ago, we were living in an apartment complex. Both my wife and I were competitive shooters, so we would go in and out of the apartment with our firearms, in proper cases of course. On Halloween our cars were the only cars in the lot that did not get the windows soaped.