I haven't seen an analysis that Heller negates property bans. Law articles, books - haven't seen it.
SCOTUS decisions and legislation have affected businesses (I guess a rental is a business) when it comes to discrimination against protected classes. But gun ownership and carry is not protected in that fashion.
The argument that businesses can ban CCW would be used to support the same in apartments or rental houses. Heller applies to the government.
Specific legislation or a SCOTUS decision would be needed but I doubt SCOTUS would go near this.