In the latest version of iOS* you can set a text tone for a caller, also change the vibrate settings, and also make it an Emergency Bypass, so that it will alert you even if your phone is set to do not disturb.
Make sure the phone number is set up in a contact as a mobile phone, then 'edit' the Contact and click on Text Tone where you can set the options.
*only looking at that one, don't know about earlier iOSs.