From Snopes:

Certainly Arnold Palmer's wife never proclaimed on the Tonight Show that she kissed her husband's balls for luck: the wife of a pro golfer, not herself a celebrity, simply wasn't the type of guest Johnny Carson invited to appear on his highly-rated talk show. (Indeed, Arnold Palmer's representative confirmed to us that Mrs. Palmer was never a guest on that program.) As for Arnold Palmer himself, comedian Jay Leno asked him about the legend in 1994, a few years after taking over as permanent host of the Tonight Show following Carson's retirement in 1992, and Palmer indicated to him that the story was based on nothing more than a joke deliberately told by Carson:
Leno: ... apparently Johnny said, "Is there anything your wife does to bring you good luck?"

Palmer: No, Johnny said, "Does your wife kiss your balls before you go to play?" and I said, "I don't even go to bed without pajamas."

Leno: I thought that was a tactful way ... but thanks for getting right to the point. So we cleared that up. That's like a famous one, like Jack Benny's, "Your money or your life ... I'm thinking it over." I wanted to find out ... so it is true?

Palmer: There you've got it. And I don't want to hear about it any more.