The film is inspired by 1980s TV series of the same name and stars Gosling as Colt Seavers, a top Hollywood stuntman down on his luck after an on-set accident
Cosby, 77, has never been charged and his lawyers have said the assault claims were "discredited" and "defamatory".
Still, the allegations have dealt a setback to a career comeback for the actor and comedian.
NBC cancelled a project in development with Cosby while Netflix postponed a stand-up comedy special.
Cosby is slated to appear at a sold-out show in Melbourne, Florida, Friday and a show in Yakima, Washington, next week.
He performed a comedy show in Nassau, Bahamas, on Thursday.
Cosby has refused to address questions about the allegations.