Lisa Bloom, Dickinson's attorney, had been scheduled to depose Cosby on Nov. 23. She was slated to depose Cosby's former attorney, Martin Singer, on Nov. 19.
"Mr. Cosby has employed several law firms with a combined total of over 700 lawyers in an attempt to avoid answering questions from me under oath in our case," Bloom said in an email following the ruling. "We are confident that once the court of appeals hears full argument on the issues it will allow the deposition of Mr. Cosby and his attorney to go forward."
Dickinson sued Cosby in May after his lawyer at the time issued a statement denying her allegation that the comedian raped her and calling it "a lie." The model's lawsuit says the denial amounts to defamation.
Cosby has continued to deny that he raped Dickinson.
Earlier this month, Los Angeles County Superior Court Judge Debre Katz Weintraub ruled that Bloom could depose Cosby and Singer before Nov. 25. Cosby's attorneys had sought to dismiss the case.
The judge limited the deposition to evidence showing whether the comedian's denial of Dickinson's allegation that Cosby raped her in Lake Tahoe in 1982 was made maliciously. The limitation essentially prevents extensive questioning of Cosby about the 50 other women who have accused him of sexual assault or abuse.
The judge also noted that Singer would be able to assert attorney-client privilege in not answering some questions.
Last month, attorney Gloria Allred, who is Bloom's mother, deposed Cosby, 78, in a lawsuit filed by Judy Huth, who alleges she was sexually assaulted by the comedian in the 1970s at the Playboy Mansion when she was 15 years old.
After that deposition, Cosby replaced Singer with attorney Christopher Tayback.