They went wild with their signs, which I think is nice. There is no mistaking that the City of Brentwood doesn't want anyone with a gun on their park property.
Granny White Park
Concord Park, where the library is located is not posted. There are however two small (not required size) signs near the entrances of two of the walking paths.Brentwood ordinance
Sec. 42-161. Weapons and firearms generally.
(a) It shall be unlawful for any person to carry in any manner whatever, with the intent to go armed, any razor, dirk knife, blackjack, brass knucks, pistol, revolver or any other dangerous weapon or instrument.
They do not make any exceptions for someone who is authorized or entitled to carry. I'm pretty sure their law goes back to at least 1977.
It seems to me since their law is older than 1986 that TCA 39-17-1314 allows them to prohibit weapons.
I wasn't able to find a Brentwood resolution prohibiting carry in parks, but most of their parks are posted. I found two which were not. So, I'm not even sure if I can carry there.