During Tuesday night's episode of Watch What Happens Live, Cohen challenged his close friend and fellow dad to a round of Diaper Daddies, a game in which each dad is given 45 seconds to change as many diapers as possible.
"I want to see which one of us is more skilled in the treacherous art of wiping and changing our little ones," Cohen says, introducing the game.
To kick off the competition, Cohen, who welcomed son Benjamin Allen in February 2019, and Cooper, who welcomed son Wyatt Morgan in April 2020, were each presented with a basket of baby dolls and a set of diapers.
As the timer began, both dads buckled down to quickly change each doll's diaper.
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"Diaper daddies, it's the game that's sweeping the nation," Cohen, 53, teases during the game.
At the end of the 45 seconds, Cooper won with a total of four diapers changed while Cohen finished with only "two and a half."
Watch What Happens Live with Andy Cohen/ youtube
The CNN anchor may need his diaper skills in the future as he recently told PEOPLE about the possibility of welcoming more children into his family.
"Would I want to have more kids? I would, definitely. It would certainly be nice for Wyatt to have a sibling. Yeah, it would be," Cooper, who co-parents Wyatt with ex Benjamin Maisani, said.
Speaking of his little boy, Cooper gushed that he is "so happy and giggly" these days.
"He does this thing where we go to a coffee place and he'll walk around and look at people, and once they make eye contact with him he'll laugh," the proud dad continued. "I love how he interacts with strangers and takes joy in them. I'm charmed by everything he does, annoyingly. And being there when he wakes up and taking him out of the crib, it's just the best."
"I suddenly think like, 'Oh my God, there's going to be a time when he won't let me kiss his face all over or hold his hand even,' " added Cooper. "I just want to rub his tummy right now as much as I can, because I know at a certain point he'll be like, 'Just get away from me.' "