“I like (porterhouse steak, hero sandwiches, grapefruit, et al.), but I don’t think I can eat a whole one” is a common food saying. It became so common that “I like/love (X), but I don’t think I could eat a whole one” became a popular meme about anything a person likes—not just food.
 
“I like children/kids, but I don’t think I could eat a whole one” is the most popular version. “(I like children. Couldn’t eat a whole one, but I like ‘em…” was posted to the newsgroup
rec.travel.asia on January 28, 1995. “I like cats/dogs/horses, but I don’t think I could eat a whole one” is also popular
 
The meme has been printed on many T-shirts and ecards.
 
       
Google Groups: rec.arts.sf.tv.babylon5
Can I like both B5 and Voyager?
John Shiali
1/21/95
(...) 
“Nice computer, but I couldn’t eat a whole one…..”
 
Google Groups: rec.travel.asia
Need info on Taiwan
Bob Korzeniowski
1/28/95
(...)
The key word in that sentence being “children”... (I like children. Couldn’t eat a whole one, but I like ‘em…  😉  )
   
Google Groups: comp.unix.aix
Amusing boot hang
Edward Hibbert
11/17/95
(...)
“I like mange-tout - but I couldn’t eat a whole one.” - Harry Hill
   
Herald Scotland
This clowning has to start
28 Feb 1997
(...)
Pauline says: ‘‘You can’t just put on a funny suit and be a clown. It’s not even something you can learn, it has to come from the heart. And you have to love children.’’ Tommy agrees: ‘‘Aye, but I couldn’t eat a whole one.’‘
 
Google Groups: soc.culture.vietnamese
[Laughs] One Liners III
Tuyet Pham
3/26/97
(...)
1. I haven’t lost my mind, I know exactly where I left it.
2. I know it all. I just can’t remember it all at once.
3. I like kids, but I don’t think I could eat a whole one.
 
Lulon Today (UK)
WOMAN WHO BARES ALL FOR THE SHY STARS
01:00Thursday 22 July 1999
(...)
I like kids, but I couldn’t eat a whole one, she (Ingrid Bradley—ed.) joked.
 
Google Groups: alt.talk.bollocks
I love dogs
The Naked Gonad
6/6/03
But I could’nt eat a whole one!
   
21 June 2003, Tallahassee (FL) Democrat, “Inept: Zings!,” pg. A12:
I like kids, but I don’t think I could eat a whole one.
 
Google Books
Man Walks into a Bar:
Over 6,000 of the Most Hilarious Jokes, Funniest Insults and Gut-Busting One-Liners
By Stephen Arnott and Mike Haskins
Berkeley, CA: Ulysses Press
2007
Pg. ?:
I like kids, but I don’t think I could eat a whole one.
 
Daily Mail (UK)
I just love children… but I could never eat a whole one (only kidding!)
By NORA EPHRON
Last updated at 09:30 15 February 2007
As the award-winning director and screenwriter of When Harry Met Sally, Sleepless In Seattle, You’ve Got Mail and Bewitched, NORA EPHRON is celebrated as one of Hollywood’s frankest and sharpest wits.
 
Now 65, she has written a hilarious and moving collection of essays about ageing. Here, in the last of our exclusive series, she shares her experience of bringing up her children - and takes an irreverent side-swipe at the modern concept of ‘parenting’.
 
Twitter
Dave Kent
‏@VelvetRazor
I love puppies, but i couldn’t eat a whole one.
12:10 PM - 4 May 2007
   
Daily Mail (UK)
Kids? I love them but I couldn’t eat a whole one
Last updated at 09:14 17 September 2007
Responding to the return of C4’s Supernanny and Jo Frost, the Non-Domestic Goddess feels it is about time she shared her own child-rearing expertise.
 
Google Books
More One Liners, Jokes and Gags
By Grant Tucker
London: The Robson Press
2013
Pg. ?:
I like children, really, I do. But I don’t think I could eat a whole one.
 
Google Groups: 5i05biq62yfn5vbh
I Love Cats But I Can’t Eat a Whole One T-Shirt 3XL Black
Hatchett
6/29/14
 
Google Books
Get Started in Stand-Up Comedy
By Logan Murray
London: John Murray Learning
2015
Pg. ?:
For example, the previous day you might have written: ‘I like children’ and today you might supply the afterthought (as W.C. Fields did) ‘but I couldn’t eat a whole one’ or ‘they’re much easier to beat at kickboxing’.