“April showers bring May flowers” is a proverb that dates to the 16th century. A popular Thanksgiving joke is:
 
Q: If April showers bring May flowers, what do May flowers bring?
A: Pilgrims.
 
The joke has been cited in print since at least 1959. May flowers don’t always bring Pilgrims, however. “Mosquitoes” was an answer in 1962 and “June bugs” was an answer in 1980.
 
   
Wikipedia: Mayflower
The Mayflower was the ship that transported the first English Separatists, known today as the Pilgrims, from Plymouth to the New World in 1620. There were 102 passengers, and the crew is estimated to have been about 30, but the exact number is unknown. This voyage has become an iconic story in some of the earliest annals of American history, with its story of death and of survival in the harsh New England winter environment. The culmination of the voyage in the signing of the Mayflower Compact was an event which established a rudimentary form of democracy, with each member contributing to the welfare of the community.
 
20 March 1959, Alamogordo (NM) Daily News, “Wailin’ Wall” by Weepin’ Willie, pg. 1, col. 1:
Laugh Lines
If April showers bring May flowers, what do May flowers bring? To which the obvious answer is—pilgrims.
 
14 May 1962, The Sentinel-Record (Hot Springs National Park, AR), pg. 4, col. 1:
If “April showers bring May flowers,” what do May flowers bring? Mosquitoes, most likely!
 
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June 1962, Boys’ Life, “Think and Grin,” pg. 74, col. 2:
She: If April showers bring May flowers what do May flowers bring?
He: What?
She: Pilgrims. — Joseph DeMarinis, Union City, N. J.
 
23 July 1962, Boston (MA) Traveler, “Flowers Bloom On The Hill” by Peggy Brown,pg. 11, col. 1:
If April showers bring May flowers, what do May flowers bring? “Pilgrims,” somebody quipped.
 
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October 1980, Boys’ Life, “Think & Grin,” pg. 81, col. 2:
Sam: If April showers bring May flowers, what do May flowers bring?
Gus: What?
Sam: June bugs.—Benji Bladh, Alton, Utah.
   
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November 2003, Boys’ Life, “Think & Grin,” pg. 53, col. 2:
Dink: If April showers bring May flowers, what do May flowers bring?
Duff: What?
Dink: Pilgrims and allergies. — Edward Kardish, Arnold, Md.
 
Google Books
A Dictionary of Proverbs
Edited by Jennifer Speake
New York, NY: Oxford University Press
2008
Pg. ?:
2001 Washington Post 1 July F1 If April showers bring May flowers, what do June brides bring?
 
Google Books
Corny Thanksgiving Jokes to Tickle Your Funny Bone
By Linda Bozzo
Berkeley Heights, NJ: Enslow Publishers
2013
Pg. 7:
If April showers bring May flowers, what do May flowers bring?
Pilgrims.