A bowling alligator pun is:
Q: What do you call an alligator who goes bowling?
A: An alley gator.
The joke has been cited in print since at least 1980.
24 July 1980, Lexington (KY) Herald, A Page Just For Kids, pg. C-4, col. 5:
What do you call an alligator who goes bowling? An alley gator!—Paul Ladwig, 9. Lexington.
21 April 1985, Newsday (Long Island, NY), Kidsday, pg. 47, col 3:
What do you call an alligator who goes bowling?
An alley gator.
-- David Fischer, Bayside
17 August 1986, The Plain Dealer (Cleveland, OH), Comic Section, pg. ?, col. 3:
What do you call an alligator that bowls?
An Alley Gator.
Animal Jokes & Riddles
By Jeffrey S. Nelsen
New York, NY: Checkerboard Press
What’s big and green and likes to bowl?
Fabulous and Funny Clean Jokes for Kids
By Bob Phillips and Steve Russo
Eugene, OR: Harvest House Publishers
Myrtle: What do you call a crocodile that enjoys bowling?
Winifred: I have no clue.
Myrtle: An alley-gator.
28 March 1997, The News Journal (Wilmington, DE), “Just For Laughs,” HoursPlus sec., pg. 21, col. 5:
Q: What do you call a crocodile that likes to go bowling?
A: An alley-gator.
Rob Palute, age 10
December 2001, Boys’ Life, “Think & Grin,” pg. 62, col. 3::
Lyle: What do you call a crocodile that is an expert bowler?
Lyle: An alley gator. — Kyle Trawick, Conroe, Tex.
What do you call a crocodile that likes to bowl? An alley-gator!!! #PopsicleStickJokes
5:45 PM - 31 Mar 2010
What do you call a crocodile that likes to go bowling? ---An alley gator.
2:44 AM - 23 Sep 2010