Again Gmail is in-app. Open Gmail, menu button (three dots top right), settings, email account you wish to change (example@gmail.com), Inbox sound & vibrate, Sound. You can also set seperate notifications for certain labelled messages too if you have a rule to go straight to an email by scrolling down to manage labels in the settings for the account, select the label and choose notification for that too.
I'm sure you can for the other stock email app for outside email addresses but I don't use it so wouldn't know how to go about it but I imagine should be something along the same lines. Hope this helps.
