I had this problem too on an Apple aluminium bluetooth keyboardand and spent a long frustrating time on it before I cracked it.
If you have a Mac in the home. Select preferences and disconnect the keyboard. Shutdown the Mac and leave it off. I found this to be my problem, as the keyboard was conflicting with the Mac during the "pairing" phase.
1. Turn off the keyboard "hard' by pressing the on button for about 5 seconds. the light will first come on then go off.
2. Go to Settings on the Apple TV. Then selectn General, then select Bluetooth, Apple TV will start searching for a device.
3. Turn on the keyboard by pressing the on button briefly. The search will discover the keyboard immediately. Using the Apple TV remote, scroll down to the, "Keyboard found Not paired". Press select on the Apple TV and a 4 digit number will appear after pairing. Enter the number using the keyboard and press select on the Apple TV remote. The keyboard will be set for controlling the Apple TV.
If you still have a problem at the pairing stage, shut down any blue tooth product in the home and start again by switching of the key board hard for a few seconds and then press the on button.
Good luck.