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"Ruddy also agreed that the script wouldn’t include “Cosa Nostra,” another name for the mafia"

Although Corleone does greet Barzini right at the beginning, at Connie/Carlo's wedding, by saying "Benvenuto a casa nostra" -- "Welcome to our house" -- which I always figured was a mild pun of sorts on the writers' parts.

Also mentioned in godfather part 2: https://m.youtube.com/watch?feature=youtu.be&t=4m26s&v=L6DkV...

From the article:

"So Paramount agreed and [the League] thought it’d won this great victory despite the fact there was only one use of ‘mafia’ in the script.”

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