Here's a typical letter with the News Director's thoughts in italics:
"I'm an award winning reporter..."
Yeah, everyone's got awards of some sort
"I'm a take-no-prisoners reporter who fights for the lead story..."
Geez, I sure as hell hope so
"I've broken some big stories during my two years here..."
Uh, that's what reporters do
"I'm a terrific writer..."
Okay, got the point?
The one thing News Directors don't need is a reporter who thinks he or she is the greatest thing since sliced bread. Your current ND may think you're great, you may have a wall full of awards, you may indeed be a terrific writer, but no ND is going to believe it until you actually work in his newsroom.
Keep your cover letter modest when talking about yourself. You still want a clever cover letter, but be humble when writing it. Let your tape showcase your on-air talent. If you're as terrific as you think you are, the ND will be able to see it on your tape.