So, I bought a radio room recently and its not boosting my dweller's charisma
The Radio Studio isn't supposed to increase Charisma. It does two things:
- Attract more dwellers to your vault
- Increase the happiness of your dwellers.
It does not increase stats, and nothing anywhere implies it should. The room you may be looking for is the Lounge, which is unlocked with 40 dwellers and slowly increases the charisma of anyone placed in it.
It only boosts happiness when played inside the vault. You can do that by turn it off from playing in the wasteland.