“What has four legs and flies?” is a riddle that has had many answers. “Two ducks” was an answer in 1918. “A dead horse” was an answer in 1922. “Two pairs of pants” was an answer in 1923.
 
“The backyard picnic table” is an answer that was cited in print in 1971.
 
“What has four wheels and flies?”/“A garbage truck” and “What has 18 legs and catches flies?”/“A baseball team” are similar riddles.
 
 
3 September 1918, St. Louis (MO) Post-Dispatch, Daily Magazine, Comic Page, pg. 1, col. 3:
Of Course.
“What has four legs and flies through the air?”
“What?”
“Two ducks.”
 
Chronicling America
2 November 1922, Norwich (CT) Bulletin, pg. 9, col. 3 classified ad:
I HAD TO LAFF—A fella sez what haz four legs and flies? an’ I sex I dunno, he sez a dead horse; mebe he’s right but I never seen a horse fly.
 
16 December 1923, The Sunday Herald (Boston MA), “Nuts to Crack” by Billy Squirrel, sec. E, pg. 1, col. 5:
What has four legs and flies?
Answer—Two pairs of pants.
     
Old Fulton NY Post Cards
17 January 1924, Variety, pg. 32, col. 1:
Harry and Denis Du For, billed as “The Dancing Ideale,” had things their own way in second spot as regards comedy, although they got their laughs almost entirely from the balconies. The floor was stolid to their stuff. Their pet gag was the riddle, “What has four legs and flies?” There are two answers to this riddle which have stood since Sheridan’s ride. One Is “Two canaries.” The second is “A dead horse in the summer.” The Du For Brothers used the latter gag answer, and it didn’t do well in a family house, especially a house that used to bar even a reference to a mother-in-law for fear somebody might be displeased. The dead horse brigade was not strongly in evidence Monday night and the gag would have been better if left out.
 
17 July 1931, Suburban Star (Blue Island, IL), “Star Lights,” pg. 1, col. 1:
What has four legs and flies? Every chair, table, bed and stove, these days, regardless of screens.
 
9 March 1971, Tipton (IN) Daily Tribune, “Grassroots Gleanings” by Bill Stokes, pg. 20, col. 1:
The Osceola County Tribune of Sibley, Iowa offers this riddle: What has four legs and flies?
Answer: The backyard picnic table.
 
Google Books
Comedy High and Low:
An Introduction to the Experience of Comedy
By Maurice Charney
New York, NY: Oxford University Press
1978
Pg. 21:
Sometimes the questions go in series, with an ascending (and possibly off-color) climax. “What has four wheels and flies? A garbage truck.” “But what has four legs and flies? Two pairs of pants.”
 
4 June 1979, Newsday (Long Island, NY) “Smiles,” Kidsday, pg. K9, col. 3:
What has four legs and flies?
A picnic table.
—Lawrence Lapitsky, Babylon
 
Google Books
The Everything Kids’ Gross Jokes Book:
Side-splitting Jokes That Make Your Skin Crawl!
By Aileen Weintraub
Avon, MA: Adams Media
2005
Pg. 44:
What has four legs and flies?
A dead cow.
 
Google Books
Penguin Pocket Jokes
By David Pickering
New York, NY: Penguin Books
2006
What has four legs and flies?
A picnic table.

What has eight legs and flies?
A dead donkey lying on a picnic table.
 
Google Books
Man Walks into a Bar:
Over 6,000 of the Most Hilarious Jokes, Funniest Insults, and Gut-Busting One-Liners
By Stephen Arnott and Mike Haskins
Berkeley, CA: Ulysses Press
2007
Pg. 205:
What has four legs and flies? A dead horse.
 
Google Books
The Mammoth Book of One-Liners
By Geoff Tibballs
London: Constable & Robinson Ltd
2012
What has four legs and flies?
A dead hamster.
 
Google Books
The World’s Greatest Collection of Clean Jokes
By Bob Phillips
Eugene, OR: Harvest House Publishers
2013
Pg. 67:
What has four legs and flies?
A picnic table.