Prohibition in the United States (1920-1933) resulted in the following popular parody rhyme, cited in print since at least June 1920:
 
Thirsty days hath September
April, June and November
Every month’s a thirsty one
Except February alone,
February (to its praise)
Has only twenty-eight dry days,
But Leap-year coming once in four,
Feb. must thirst for one day more.
—Leslie’s Weekly.
 
 
Wikipedia: Thirty days hath September
Thirty days hath September is a traditional English mnemonic rhyme, of which many variants are commonly used in English-speaking countries to remember the lengths of the months in the Julian and Gregorian calendars. Here is one version of the rhyme, attributed to Mother Goose:
 
Thirty days hath September,
April, June, and November.
All the rest have thirty-one,
Excepting February alone,
And that has twenty-eight days clear,
And twenty-nine in each leap year.
(...)
And another parody:
 
Thirsty days hath September,
April, June, and November;
All the rest be thirsty too;
Except for he who hath home brew!
 
Google Books
June 1920, The American Blacksmith, pg. 226, col. 2:
Thirsty days hath September
April, June and November
Every month’s a thirsty one
Except February alone,
February (to its praise)
Has only twenty-eight dry days,
But Leap-year coming once in four,
Feb. must thirst for one day more.
—Leslie’s Weekly.
   
30 September 1921, Ann Arbor (MI) Times News, pg. 4, col. 3:
Thirsty Days.
Thirsty days hath September,
April, June, and November;
All the rest be thirsty too;
Except for him who hath home brew.
—Allen.
     
Google Books
15 October 1921, The Mixer and Server (Cincinnati, OH), pg. 29, col. 1:
Frederick Lehman, St. Louis, Mo., formerly Solicitor General of the United States, is accused of springing the following at one of the little parties held during the week of the convention:
 
Thirsty days hath September,
April, June and November
All the rest are thirsty, too,
Unless you make your own home-brew.
 
12 May 1922, New York (NY) Times, “Wet verse cheered at women’s forum”:
Thirsty days hath September, April, June and November, all the rest are thirsty, too, unless you make your own home brew.
 
Google News Archive
18 June 1922, Youngstown (OH) Vindicator, pg 4C, col. 4:
PROHIBITION BLUES
There’s a bulletin gotten out by the Congress Lake Club, Hartville, Ohio called the “Club Chats” that is among the most interesting of its kind to be found anywhere. In the current issue it is stated that the favorite song heard in the locker room these days is as follows:
 
“Thirsty days hath September,
April, June and November,
All the rest have thirsty ones,
With the exception of February,
Which usually has twenty-eight
Thus making it difficult
For the bootleggers
To earn as much as usual.”
 
Google News Archive
1 September 1922, Border Cities Star (Windsor, Ontario), “Starbeams,” pg. 4, col. 3:
Thirsty days hath September
April, June and November;
All the rest are thirsty, too,
‘Less you make your own hoe brew.