In the F.A.Q. section of J.K. Rowling's Official Site, she stated that Sirius was "around twenty-two" when he was imprisoned in Azkaban. دیا that he was imprisoned shortly after 31 October 1981 and attended Hogwarts from 1971 to 1978, Sirius would have been born between 1 September 1959 and November 1959.
I only know he is born in either 1959 یا 1960 and that is based on James' and Lily's birthdates. I don't think I ever read everything about his تاریخ of birth and I checked the Harry Potter lexicon and they don't know it either (and usually, when it is ever mentioned, they have it on their site).