Of American-English origin, dad-joke denotes a joke of the type said to be told by fathers, i.e., a hackneyed, embarrassing or unoriginal joke.
—Cf. also dad-dancing.

These are, in chronological order, the earliest occurrences of dad-joke that I have found:

1-: From Don’t ban the “Dad” jokes; preserve and revere them, by Jim Kalbaugh, editor/publisher of the Gettysburg Times (Gettysburg, Pennsylvania), published in that newspaper on Saturday 20^th June 1987:

A young joke teller, freshly certificated by a comedy workshop, made his debut on network television, boldly suggesting that all “Dad” jokes be banned.
“Dad” jokes, he pointed out, are synonymous with “bad” jokes, or “baddddddd” jokes.
As we approach Father’s Day, I would like to propose that “Dad” jokes not be banned. They should be revered, preserved.
Sure, “Dad” jokes make kids, and wives, wince.
You know the scenario. A Dad is driving his kids, and their friends. And, when they pass a cemetery, the Dad says: “How many dead people are in there?”
No answer, but the offspring cringe, and moan, and then mime the response: “All of them.”
A polite chuckle from the guests only spurs the Dad on.
“Why do they have a fence around the cemetery?”
“Oh, no,” someone, not a visitor, moans.
But, Dad presses on: “Because people are dying to get in there.”
A few giggles is all the Dad needs to think he’s on a roll.
“What did one gravestone say to another?”
“Don’t take me for granite.”
Landmarks often set off “Dad” jokes.
A drive past the Round Barn may prompt the question from a Dad, “Ever know why the dog went crazy in that barn?”
“He couldn’t find a corner to sleep in.”
The “Dad” joke is one reliable aspect of fatherhood. It’s what children, and Moms, can count on from a “Dad.”
It’s as sure as three meals a day at home.
Geoffrey W. Taylor of Carroll Valley is a Dad, an extraordinary one. Multiple sclerosis has paralyzed him, shrouded his sight and silenced his vocal chords, but his humor, like his mind and heart is strong.
It’s humor that keeps him going. Getting a laugh is one link with his family and friends. In barely audible, but labored, spurts of breath, he whispers jokes to his wife, and children.
He’s a man who couldn’t remember a joke, much less tell one, a few years ago. In the early stages of his illness, he found himself sprawled on the bathroom floor, unable to move while his family was away for a few hours. He was swept by a flood of tears from anger and frustration at not being able to get up.
Then, suddenly, he started to remember jokes.
When his family finally came home, they heard him, howling with laughter at his own jokes, those bad, “Dad” jokes, like:
“Knock, knock”
—“Who’s there?”
“Old lady.”
—“Old lady who?”
“I didn’t know you could yodel.”
Geoff Taylor can’t yodel, but he can write. He has just finished a book of humor for those who are ill, especially the terminally ill.
A veteran of eight hospitalizations, Mr. Taylor has observed that “hospitals are loaded with staff and patients who long for humor.”
His yet unpublished book, he hopes, will help somebody else get through an ordeal of trying to cope with illness that can floor them.
There is a special draw and durability to the “Dad” joke. They not only last for a whole generation, but they are passed on to those offspring who become Dads, and they pass them onto to a succeeding generation.
Somehow they always work, in their own way.
Here’s one:
There was a man who saw a boy with a banana in his ear.
He asked the boy, “Why do you have a banana in your ear?”
The boy replied “What?”
“I asked you,” the man said, “Why you have a banana in your ear?”
“What?” the boy asked, a second time.
The man repeated the question.
“Sorry,” the boy said, “I can’t hear you cuz I have a banana in my ear.”
Talk about bananas . . .
One man asked, “Did you hear about the guy who went to Europe on a banana boat?”
—No, why did he go to Europe on a banana boat?
“Because it appealed to him.”
Well, “Dad” jokes never lose their appeal, especially to Dads, and succeeding Dads, and Dads who succeed them.
It’s one of the great traditions of fatherhood worth preserving.

2-: From 8-year-old teller is a stand-up guy, by Allan Johnson, published in the Chicago Tribune (Chicago, Illinois) of Thursday 22^nd September 1988—here, Corey Carrier attributes the dad-jokes he tells to his own father:

“His credits include the movie ‘The Witches of Eastwick’ and the TV show ‘The Equalizer.’
[…]
“Ladies and gentlemen, Mr. Corey Carrier!”
[…]
Corey Carrier, 8, started performing on stage when he was about 2½. In addition to various modeling assignments, a handful of commercials, two or three television movies and the aforementioned movie role, Corey performs a 10-minute stand-up comedy routine. He started telling jokes at age 4.
“You want a joke? I’ll give you a joke. My dad wanted to be a comedy writer. I told him, ‘Right—and Gary Hart wanted to be president.’” Firmly grasping the microphone and its stand, he continued, “Listen to the jokes my dad wrote: Why do bees hum? ’Cause they don’t know the words.
“I guess you can call this safe comedy.”
The crowd of about 250 laughed politely, as if they were still trying to track with what they were seeing on stage. Meanwhile, the kid went on with this line of dad-jokes as if he were a seasoned veteran working a tough room:
“How do you start a teddy-bear race? Say ready-ted-go? . . . Now I know what child abuse is.”
Out of the mouth of babes. . . .

3-: From Howie Mandel plays Valley Forge, by Jim Gladstone, published in The Philadelphia Inquirer (Philadelphia, Pennsylvania) of Monday 6^th November 1989:

Opening with a loose-limbed routine on childbirth, Howie Mandel established an accidental motif for the first of his two performances at the Valley Forge Music Fair on Saturday night. It was the night of the killer dad jokes.
That’s not to say that the mush-faced comic actor who played delightful Dr. Wayne Fiscus on television’s late, lamented St. Elsewhere is following in the yuk-fest footsteps of fellow tube doc Bill Cosby. No, Mandel doesn’t tell charming, gently humorous tales about being a dad; he spouts the groaningly goofball puns and one-liners that are the providence of proud papas everywhere.