An elevator riddle is:
 
Q: What did one elevator say to the other elevator?
A: “I think I’m coming down with something!”
 
The riddle has been cited in print since at least 1972, when it was printed in many newspapers.
 
     
21 October 1972, The Clarion-Ledger (Jackson, MS), “Mini Jokes,” The Mini Page, pg. 3, col. 1:
Q. What did one elevator say to the other elevator?
A. I think I’m coming down with something.
Jim Hamric Owen
Ackerman
 
9 June 1973, Indiana (PA) Gazette, “Mini Jokes,” The Mini Page, pg. 3, col. 1:
What did one elevator say to the other elevator?
I think I’m coming down with something.
Donna Patterson—Clymer
 
5 October 1980, Newsday (Long Island, NY), “Smiles,” Kidsday, pg. M11, col. 3:
What did one elevator say to the other elevator?
I think I’m coming down with something.
—Maryanne Spiezio, Brentwood
 
Google Books
May 1983, Boys’ Life, “Think & Grin,” pg. 74, col. 1:
Gene: What did one elevator say to the other elevator?
Dean: I don’t know. What?
Gene: I think I’m coming down with something.—Eugene Goldberg, Bronx, N.Y.
 
Google Books
Super Sick Jokes and Riddles
BY Joseph Rosenbloom
Illustrations by Sanford Hoffman
New York, NY: Sterling Publishing Company
1990
Pg. 34:
What did one elevator say to the other elevator?
“I think I’m coming down with something!’
 
Google Books
How Do You Get There?:
A Book of Transportation Jokes
By Jill L. Donahue
Minneapolis, MN: Picture Window Books
2007
Pg. 17:
What did one elevator say to the other?
“I think I’m coming down with something.”
 
Twitter
AN†HONY DOES
‏@anthonydoes
Q: What did one elevator say to the other?
A: I think I’m coming down with something!
7:17 AM - 17 Feb 2009
 
Google Books
Wise Crackers:
Riddles and Jokes about Numbers, Names, Letters, and Silly Words
By Michael Dahl
Mankato, MN: Picture Window Books
2011
Pg. 57:
What did one elevator say to the other elevator?
“I think I’m coming down with something.”
 
Google Books
The Super, Epic, Mega Joke Book for Kids
By Whee Winn
Grand Rapids, MI: Zonderkidz
2016
Pg. ?:
What did one elevator say to the other elevator?
I think I’m coming down with something.