“Money can’t buy happiness” is a proverb that has been cited in English since at least 1821. There have been many jocular additions and variations to the proverb.
 
“What good is happiness if it can’t buy you money!” was printed in The Arizona Republic (Phoenix, AZ) on June 22, 1950. “What good is happiness? It can’t buy you money” was printed in Carpenter magazine in 1950. Authorship is unknown.
   
“What good is happiness?” became slightly changed to “What’s the use of happiness?” by at least 2003.
 
English-born American comedian Henny Youngman (1906-1998) used the joke in the 1970s and included it in his 1994 book, but there is no evidence that he used it as early as 1950.
 
 
Wikipedia: Henny Youngman
Henry “Henny” Youngman (original Yiddish surname Yungman; 16 March 1906 – 24 February 1998) was an English-born American comedian and violinist famous for his mastery of the “one-liner”; his best known one-liner being “Take my wife ... please”.
         
22 June 1950, The Arizona Republic (Phoenix, AZ), pg. 2, col. 1 ad:
Cynical suggestion for a framed motto,  to be worked in cross-stitch, framed, and hung over the desks of busy executives: “What good is happiness if it can’t buy you money!”
(Clark Smith car dealership.—ed.)
   
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Carpenter
United Brotherhood of Carpenters and Joiners of America
Volume 70
1950
Pg. 17:
FROM ONE PHILOSOPHER TO ANOTHER “Happiness is the greatest desire of mankind,” says a famous English philosopher in his newest book. To which Joe Paup replies, “What good is happiness? It can’t buy you money.”
     
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Advertising Agency and Advertising & Selling
Volume 45, Issues 7-12
1952
Pg. 73:
You might as well have done with it and join up with the scoffer who once asked, “What good is happiness? It can’t buy you money.”
 
10 December 1953, The Oregonian (Portland, OR), pg. 16, col. 1:
A PHILOSOPHER once said, “What good is happiness, it can’t buy you money!”
(Fred Meyer stores.—ed.)
 
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Time
Volume 62
1953
Pg. 72:
A PHILOSOPHER once said, “What good is happiness, it can’t buy you money!”
   
7 February 1971, Sunday News & Leader (Springfield, MO), pg. D3, col. 4 ad:
He (Uncle Chud Chutney—ed.) said, “what good is happiness? It can’t buy you money.”
(Jones Co. Realtors.—ed.)
 
11 July 1976, Sunday Plain Dealer (Cleveland, OH), “Henny Youngman: His work’s no joke” by Jane Scott, sec. 4, pg. 17, col. 1:
“What good is happiness? It can’t buy you money.”
   
Google Books
Henny Youngman’s Bar Jokes, Bar Bets and Bar Tricks
By Henny Youngman
New York, NY: Wings Books
1994
Pg. 74:
What good is happiness? It can’t buy you money.
 
23 January 2003, Daily Mail (London, UK), “The Case for a Ministry of Mirth” by Keith Waterhouse, pg. 14:
WHAT’S the good of happiness? - it can’t buy you money. Thus ran a cynical aphorism of my youth. I return to it as my text for today.
         
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OT: Quotes of famous people
Sally
8/13/03
(...)
What’s the use of happiness? It can’t buy you money.
(Henny Youngman)
 
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The Jewish Quarterly
Issues 209-212
2008
Pg. 17:
What’s the use of happiness? It can’t buy you money. (Henny Youngman)
 
Google Books
Happiness
By iMinds
iMinds Pty Ltd
2009
Pg. 1:
“What’s the use of happiness? It can’t buy you money.” - Henny Youngman
 
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Henny Youngman: What’s the use of happiness? It can’t buy you money. | #Quotes
4:53 PM - 5 May 2018