I got it to work!
Verbatim 97537 Wireless Bluetooth Mobile Keyboard pairing on a T-Mobile G2 running Gingerbread.
I got it to work on my T-Mobile G2 running Gingerbread Android version 2.3.4. It is not an easy connect or obvious. The trick is that I had to un-pair and pair again the keyboard each time I want to use it. It doesn't work unless it's a fresh pairing each time.
1. Go to the Market and download and install BlueKeyboard JP. I've currently got version 2.1.6.
2. Go to Settings/Language & keyboard. Enable BlueKeyboard JP. Select BlueKeyboard JP settings. There are a few nice tutorials on You-Tube for pairing a Bluetooth keyboard to your Android with this app.
3. Go to Bluetooth settings. Pair bluetooth keyboard. Turn on Bluetooth. Scan for devices. Turn on the Verbatim keyboard. Set the "Pairing" button on Verbatim keyboard. If there is a previous pairing, you need to Unpair the keyboard and redo the pairing and the keycodes on the phone and the keyboard. You should see "Verbatim Keyboard" "Paired but not connected."
4. Go to a Google search box. Long press and hold, select Input Method of BlueKeyboard JP. You might see a message saying you are "Connected..." then a pause and "Connected." Type on the keyboard and see your keystrokes appear in the search box.
If if starts saying
Please don't touch keyboard.
and tries 3 times, it's not going to work. Redo the pairing again.
I almost gave up on this, but I'm happy I found a sequence of steps that works for me.