At the moment, as per the thread title, eBay are NOT allowing Google as an payment option NOR even (according to eBay Forums) allowing it to be mentioned in listings. Your best bet is when you have items up for auction, to monitor it closely at the end and contact the buyers with a Google Checkout invoice straight away (dead easy, you need their email and amount to pay, and just add a quick description of what it is - say, item title and/or number).

If they pay by PayPal then so be it but I get a lot of buyers saying they can't get PayPal to 'work' whereas Google seems a matter of just entering your credit card details and address and confirming your payment and that's it. On your side you have an option on Google to instantly charge their card or the default is that you do this - just a button click. I use the latter simply because I use it on my new website and for stock control reasons I can refuse a payment if someone orders more than I can supply straight off.