Welcome to Android Central! Which messaging app are you using, the stock Messaging one?
I use Hangouts for SMS, and one possible way is to do the following:
1. After you get at least one text message from the email address, go to that conversation.
2. Tap the Menu button, then People & Options.
3. Make sure Notifications is turned on for the conversation, and then tap Chat Message Sound to select a specific tone.
Now, the next time you get a text from that email address (which will be added on to the conversation), it should play that specific notification tone.