From The Routledge Dictionary of Modern American Slang and Unconventional English by Tom Dalzell, 2008:

goombah noun
a loyal male friend; an Italian-American US, 1954
An Italian-American usage, sometimes used in a loosely derogatory tone.

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Here's another story from early TV, circa 1954-56, from Take It from the Big Mouth: The Life of Martha Raye by Jean Maddern Pitrone, 1999:

[Retired boxer Rocky] Graziano ... found that "Marta" [Martha Raye] frequently said and did crazy things (ad libs) that at first disconcerted him. Once she suddenly addressed him as "Goombah." Rocky did a double-take, then realized that he was the Goombah to whom she was referring. Fram that time, Rocky became known as Goombah on the Martha Raye Show.

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From Six to Five Against (fiction) by Jeff Sherratt, 2004:

"Hey Goombah, whaddya know, whaddya say?"
Luigi, the owner of Luigi's Italian Deli on Paramount Boulevard, greeted me at the door. He always said the same thing when I stopped for a pizza. I wasn't sure what goombah meant, but he called all his customers goombah, even the Italian ones. It must have been okay; they kept coming back.

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From The Annotated Godfather: The Complete Screenplay by Jenny M. Jones, 2007:

[from the screenplay:]
WOLTZ: ... I don't care how many dago, guinea, wop, greaseball goombahs come out of the woodwork.

[in a sidebar on the same page:]
Puzo's novel doesn't pull any punches with Woltz's dialogue. He yells: "I don't care how many guinea Mafia goombahs come out of the woodwork."... (Italics added). The term Mafia doesn't appear in the film.

[So "Mafia" is more offensive than "dago, guinea, wop, greaseball"? and "goombah" is neutral?—JD]

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From The Italian American Experience in New Haven by Anthony V. Riccio, 2006:

In "Il Padrino," or "The Godfather," the traditional Italian-American "compare," or godfather, became a made-for-movie godfather with a sinister side as head of a gangster family. After the huge commercial success of "The Godfather," and the string of wise-guy movies of the same genre that followed during the '80s and '90s, the word "compare" evolved into the phonetically spelled word, "goombah." "Goombah" has now become the modern catch phrase for the decades-old stereotypical Italian-American wise guy starring in the latest generation of gangster movies the public has come to expect, a disparaging name casually injected into conversations referring to anyone of Italian ancestry.