A car riddle was published in Bennett Cerf’s Book of Animal Riddles (1964):
 
Q: How do you stop a dog from barking in the back seat of a car?
A: Have him sit in front with you.
 
“Barking” is sometimes replaced with “howling.” “How do you stop a dog howling in the back of a car? Put him in the front” was posted on Twitter on August 23, 2009.
 
“How do you keep a dog from barking in your front yard?”/“Put him in your back yard” and “How do you stop a dog from barking in the back yard?”/“Put it in the front yard” are similar dog riddles.
   
       
Google Books
Bennett Cerf’s book of animal riddles
Bennett Cerf
Random House, Sep 1, 1964 - Games - 62 pages
Dogs, turtles, hummingbirds, snails, and rabbits are some of the subjects of these clever, simple riddles. They are masterfully illustrated with McKie’s bold line drawings.
 
19 September 1964, Cincinnati (OH) Enquirer, “Animal Riddles” by Bennett Cerf, “This Week” magazine, pg, 10:
How do you stop a dog from barking in the back seat of a car?
Pg. 12:
Have him sit in front with you.
 
8 November 1964, Washington (DC) Post, “A Is for Animal And C’s for Care” By the Gesell Institute,” pg. C2:
Anyway, we can recommend Bennett Cerf’s “Book of Animal Riddles” (Random House):
 
“How do you stop a dog from barking in the back seat of a car?” “Have him sit in the front with you,” of course.
 
Google Books
Biggest Riddle Book in the World
By Joseph Rosenbloom
Illustrations by Joyce Behr
New York, NY: Sterling Publishing Company, Inc.
1976
Pg. 246:
How do you stop a dog from barking in the back seat of a car?
Make him sit up front.
     
July 2001, Highlights for Children, “Riddles,” pg. 11:
How do you stop a dog from barking in the back seat of a car?
Have him sit in the front seat with you.
Michael Gonzales, Kentucky
 
Google Groups: alt.humor.puns
Puns of the Weak 09/27/02
Stan Kegel
9/28/02
(...)
How do you stop a dog from barking in the back seat of a car?
Make him sit up front. (Kids Jokes)
 
Twitter
Bollywood Sargam‏
@bollywoodsargam
Car and train jokes - 2561 Joke: How do you stop a dog howling in the back of a car? Put him in the front. .... http://bit.ly/7aPxK
12:47 AM - 23 Aug 2009
     
Google Books
Happy Smile:
Jokes for Kids
By Adam Smith
Lulu Press (Lulu.com)
2017
Pg. ?:
Q: How do you stop a dog barking in the back seat of a car?
A: Put him in the front seat.
 
Twitter
Lucky Score‏
@LuckyScoreNet
How do you stop a dog howling in the
back of a car?
Put him in the front.
#Joke from #CarAndTrainJokes in #Jokes, #Humor and #Satire
8:03 PM - 17 Oct 2017