NWG.
I'm confused. I have a VZW model...
In GMail you can turn off notifications. In GMail, Menu | Settings then go you your account, and uncheck Notifications.
** If you do this, you will not have sound notifications or, a notification icon in your notification bar **.
On the VZW model, there is a silent tone already. You can leave Notifications checked. And you can select this tone.
** If you do this, you will not have sound notifications, but you will have an icon in your notification bar (indicating you have mail waiting **.
Anyway, that's how mine works.
Check to make sure your GMail program has only one account defined to it. If it has multiple accounts, then possibly you need to make these settings for multiple accounts. Sounds reasonable right? I never use the GMail mailer for anything but GMail.
If you still have a problem, you might want to consider doing the following: (I'm not responsible if you loose some mail in the process OK? So capture or print what you need to. It's likely to be still on the server, unless you've indicated you want messages deleted when you delete them on your phone... I think it works that way but don't hold me to it.).
Go into Settings for the phone, choose Application Manager, swype all the way to the right so All is displayed. Choose GMail. Uninstall updates. Then Disable.
Reboot your phone.
Go in again and re-enable GMail. I suppose you could go into the Market and perform an "Update".
Or, you could try a FDR.
You sure it is GMail that is generating a sound?
Weird.