I don't have the G9 parts list manual, but the manuals of the G5, G6 and Pro1 have a part number for the whole Rear Cover Unit that includes all the rear controls in it.
There are no part numbers for each control; my guess is that Canon doesn't sell them separatelly and you will need to buy the complete Rear Cover Unit.
Searching the web, I found a site selling spare parts that lists the following:
Canon PowerShot G9 Rear Cover.
Canon Part#:CM1-4315
$42.00
Use it as a guide, I can not guarantee that the part or its number are correct. Do your own research before buying.
See below the pictures of my Pro1 Disassembly Guide as a reference to what you may receive after buying the part. You will need to insert the single ribbon cable in the connector of the Main Board. The connector has a latch, see below how it works to hold the cable in place.
Good luck