The channel came under fire for technical glitches when it started this month.
GB News has also been victim to a few pranks, with comedian Adam Pacitti calling in and mooning live on air, and presenters tricked into appearing to say some rude words when they read out comments from listeners claiming to be called “Mike Hunt” and “Mike Oxlong”.
But McCoy has now urged people to give the new channel a chance.
“Hey. Please judge us in six months,” he tweeted.
“The audience is there - and is supportive. We are improving every day. It’s a start-up.”
Read more: Everything you need to know about GB News
He also thanked viewers for their patience, adding: “If you don’t want to watch... don’t. Sticks and stones.”
Earlier this week the broadcaster said people just needed to “grow up”.
Addressing the recent pranks on air, he said: “I’m just going to say something because if you’ve seen the papers, if you’ve seen Twitter, some people think it’s really funny to send in texts and messages on the basis that if we read them out we’ve been had.
"And you’re still doing it, and I’m watching them, and it doesn’t help anybody.”
"We’re just not going to read surnames from now on,” co-presenter Alex Phillips chimed in.
GB News launched on Sunday and promised to present news from outside the London bubble and to take a critical stance on "cancel culture" but has faced backlash for its perceived right wing stance.
In recent days several companies including Ikea, Kopparberg, Octopus Energy and the Open University have pulled their adverts from the channel, amid claims GB News does not represent their businesses values.
Critics have labelled it a British version of Fox News, the conservative American channel but GB News has rejected this.
Stop Funding Hate, which has urged businesses not to advertise on the channel, said: "GB News' multi-million pound backers can subsidise them if they want to, but that doesn't mean the rest of us have to.
"Brands are free to choose where they do and don't advertise, and the public are free to speak out and seek to influence that choice."
Watch: GB News reads out message from 'Mike Oxlong'