It turns out to be a cottage industry:

Miss LoGiudice’s accent didn’t matter when she was growing up in Howard Beach, a heavily Italian neighborhood in Queens where dropping r’s in words like doctor (doctuh) and water (wawtuh) just happens to be the way many people talk.
“I grew up with people who could be the cast of ‘Jersey Shore,’ ” Miss LoGiudice, 27, said. It was not until she got to Wesleyan University that she realized how much her speech pigeonholed her. And as a young actress who is “tall and Anglican-looking,” she worried her accent would be a roadblock. “If I had looked like Meadow Soprano,” Miss LoGiudice said, “I wouldn’t have had to worry about my accent.”...
The online Yellow Pages includes more than a dozen listings for “New York accent reduction” specialists, and searching “New York accent” and reduction or elimination on Google generates about 4,000 hits. The process typically takes at least several months, with as many as three sessions a week, and can cost from a few hundred to a few thousand dollars.

The story does not mention it, but one of the great bits in Woody Allen's "Radio Days," which ranks among my favorite movies, centers around an actress who takes diction lessons to remove her New York accent: