If the Gamebuino had an audio jack, this would be a simple task.
You would simply stick an IR led in the audio output, disable audio from the Gamebuino lib, and use the Arduino IR library. Basically you'd be making a "sound" at 38 kHz (IR signal frequency) and modulate that, just as the PWM sound of the Gamebuino is made. That'll cost you 0.2 USD
Or
Buy an "I2C IR transmitter" and stick it in the I2C. Unfortunately, the only one I found is CtrlIM by ThingM and costs 21.95 USD
http://microcontrollershop.com/product_info.php?products_id=5002