“What drink always has a cold?”/“Cough-ee.”

“Coffee” sounds like “cough-ee.” A riddle has been printed on an image:
 
Q: What drink has a cold?
A: Cough-ee.
 
“Joke of the week: What drink has a cold? Cough-ee” was posted on Twitter by Popsicle on August 19, 2009, and was popularized on Popsicle sticks.
       
 
Twitter
Kayla Q‏
@kaylarquinn
What drink has a cold? Cough-ee! Popsicle from babysitting.
8:38 AM - 10 Aug 2009
   
Twitter
Popsicle®‏
@Popsicle
Joke of the week: What drink has a cold? Cough-ee. I’ll be here all week. Be sure to tip your waitress.
9:14 AM - 19 Aug 2009
 
Twitter 
.‏
@simpliityty
WHAT DRINK HAS A COLD??????????COUGHEE!!!!!!! LOL COFFEE!!! HAHAHAH GET IT!!!!!!!!!!!!!!!!
12:38 AM - 17 Dec 2009
 
Google Groups: alt.humor.puns
What should you drink against a cold?
Hauke Reddmann
1/18/10
Coughee.
 
Twitter
BradShort‏
@BradShort
Think i just made a joke up.  “What should you drink when you have a bad cold” . . . . . . . . . . . . . . .Coughee . .
9:20 AM - 18 Nov 2010
     
Twitter 
Princeton‏
@PrincetonPierre
What drink gives you a cold? COUGHee! Be amazed and my well thought up/lame joke!
9:06 PM - 12 Feb 2011
   
Twitter
Cargo‏
@polaboi_
What drink has a cold? COUGHee lls
3:36 PM - 28 Jul 2011
   
Twitter
Noxie Javier‏
@ilovenoxie
@efm_musicplanet #4 What drink always has a cold?~~~Cough-ee! ^^
11:13 AM - 6 Sep 2011
 
Facebook
Popsicle Jokes
March 30, 2012 ·
What drink has a cold?
Cough-ee
 
Reddit—Dad Jokes
What do you drink when you have a cold? (self.dadjokes)
submitted October 25, 2015 by K3lp_Boy
Cough-ee
   
Google Books
LOL: A Load of Laughs and Jokes for Kids
By Craig Yoe
New York, NY: Little SImon
2017
Pg. 201:
Q: What shouldn’t you drink when you have a cold?
A: Cough-ee.
 
Reddit—Dad Jokes
What drink always has a cold? (self.dadjokes)
submitted January 12, 2018 by canadiain
Cough-ee