It may be impossible to know for sure. I tend to lean towards 1899, as most of the documentation tends to indicate that date. Colleen always insisted in public she was born in 1902. The question has been asked why she would say 1902 when it was 1899, especially after publishing "Silent Star," wherein she came clean about so many other myths surrounding her story.
All I can say is that with modern search techniques that would not have been available to her, I came up with enough conflicting information that I'm still not sure. I doubt Colleen would have lied about her age, as she was so frank about other aspects of her life. I can only assume that Colleen did not know the date for certain herself. A difference of 2 or 3 years would have been trivial, especially after "Silent Star." The book was ghost-written by Adele Rogers St. Johns, who helped cultivate the Colleen Moore myth. Perhaps all these factors came together to assure that the date will always be in question.