News of both the cyberattack and the admission that the website is trying to fix "technical difficulties," came via tweets from the magazine and the Twitter account @Vikingdom2016.
The alleged hacker, ThreatKing, told The Daily Dot that the site's platform was overwhelmed late Sunday.
ThreatKing told The Daily Dot he carried out the so-called "distributed denial-of-service attack" over his hatred of New York and the "many stupid people" there. It's not clear whether he had any objection to the cover photo itself or the interviews with the women.
Around 8:30 a.m. ET on Monday, the magazine said on Twitter that its site was "still down," but added people can listen to "two women's testimony about Cosby on Instagram."
Model Beverly Johnson posted a tweet saying she spoke to someone at the magazine whose email account has "also been hacked," adding "they are working to get the site back up."' She then tweeted, around 11:45 a.m. ET, that the website had been restored. However, clicking on the site still produced an error message at that time.
The July 27 issue of the magazine has a black and white cover photo showing 35 women seated in rows. The headline reads, "Cosby: The Women. An unwelcome sisterhood."
The magazine has provided a link on Twitter to its Instagram account, which has audio clips of some of the women.
Cosby, 78, has been accused by more than two dozen women of sexual assault in incidents dating back more than four decades. The entertainer has never been charged with a crime, and the statute of limitations on most of the accusations has expired.
Earlier this month, The Associated Press obtained documents that revealed Cosby acknowledging he secured Quaaludes with the intent of giving them to young women he wanted to have sex with. He never admitted to giving the drug to anyone.