The real problem with "Airline" internships, are
1.) SOME internships are only open to specific Schools i.e. United/Continental internship are open to UND, ERAU, WMU, Etc.
2.) NETWORKING! I say this because I got on as a SkyWest Intern, and I didn't qualify for the internship, after I applied.
From my experience these many years in collegiate aviation. It is about who you know, and take every opportunity that aviation student groups throw at you, from joining flight team, to doing mock interviews. Otherwise, good luck applying to all the same websites that hundreds of aviation students around the country are applying for.
3.) MAKE YOUR PERSONALITY SHINE!! I don't mean to sound so "weird" there, but this ties into networking, make someone remember you, by being yourself and outgoing.
Good Luck!