The former BBC presenter said he was labelled "bitter and twisted" earlier this week after he burst into laughter over the couple’s statement on Afghanistan, in which they said they were "speechless" about the situation.
On Thursday’s show, McCoy’s co-host Kirsty Gallacher noted that Harry and Meghan were in the news again.
McCoy, 59, quipped: "Do we need to talk about this? I get myself into trouble every time."
"You are in trouble today, he’s in big trouble," Gallacher agreed, and McCoy confessed: "I’m in trouble after what I said yesterday about them."
Gallacher then held up a newspaper article entitled "Blame of Thrones", which claimed Harry and Meghan were not impressed with the way the Palace dealt with the allegations they made in their sensational interview with Oprah Winfrey.
She read a line from the article saying: "Swipe at Queen over recollections may vary, Charles and Wills must own their part in the feud."
"That is the front cover of today’s Sun."
Gallacher then warns McCoy: "Say no more! I think you shouldn’t.
"Let’s move on to another subject."
McCoy then made a zipping his lips gesture and said: "The Duke and Duchess of Montecito..."
"Oh gosh you’ve said it now, I mean, it’s another day for you in the press. Brilliant!" Gallacher laughed.
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McCoy then said: "What was I, bitter and twisted yesterday?" he asked. "I wonder what I’ll be today?"
On Wednesday, McCoy giggled on air when Gallacher said that the Duke and Duchess of Sussex had "broken their silence to say they are speechless about the situation in Afghanistan."
"Sorry, only they would break their silence to tell us they are speechless," he said.
Watch: GB News’ Simon McCoy erupts into laughter at Prince Harry and Meghan’s Afghanistan statement