If you have multiple Gmail accounts set up in the Gmail app for iPhone and iPad, you may not need to receive push notifications for new messages for every single account. Luckily with the Gmail app, your options aren't all or nothing. You can easily choose what accounts you'd like to receive notifications for.
That's all there is to it. That specific Gmail account will obey your notification settings. Now just repeat this process with each Gmail account that you have configured specifying what notifications, if any, you'd like to receive for that account.