I use the following process to install tvOS beta profiles onto my Apple TV without having to connect it to my laptop.
- Download the tvOS configuration profile from the Apple Developer website
- Move the file to a webserver that is reachable by the Apple TV
- On the Apple TV, go to Settings -> General -> Privacy and just highlight the Share Apple TV Analytics menu item.
- Press the Play/Pause button on the Apple TV remote
- Click Add Profile
- Type in the URL of the profile on the webserver
- Follow the prompts to install the beta profile
- Restart the Apple TV when prompted
- Go to System -> Software Updates -> Update Software to install the new tvOS update.Note: On at least one occasion, I have had to turn off Get Beta Updates in order to get the beta tvOS to install.