Are you making the Jamma adaptor or are you just hooking up one you already have?
If you are making one, you will need to check the pinout of the Birdie King 2 game to see which pins you need for your cabinet.
You will need to connect:
Power
Video
Controls (trackball) -- does your Jamma cabinet have a trackball?
Audio
Coin door
These pinouts will be on one or more of the 3 connectors.