Well in Doomed Buffy states she's a Capricorn born on the Cusp of Aquarius which means she can only be born one particular day: January 19th.
That date is also supported by "Surprise", which actually aired on January 19, on Buffy's 16th birthday. Generally speaking, the show aired in "Real Time", meaning that the days and dates it aired on were
usually the same as the in-show day and date (most of the exceptions occurred, I believe, where an episode spans more than one day.) But that's not a
precisely accurate guide: For example, "Family", which centered on Tara's birthday, aired on November 7, 2000, and "Seeing Red" aired on May 7, 2002. Then, in "Help", we see Tara's gravestone with the dates November 16, 1980 - May 7, 2002. So there's a little "drift" between the air date of "Family" and her stated birth date.
By the way, speaking of "drift", the cusp drifts, also; because of the sun's/earth's/universe's movements, there is no one particular day for any given cusp, but rather a range of days where the cusp may appear in any given year - the same way that the solstices and equinoxes do not
really occur on the same days every year. That Cusp of Aquarius could fall anywhere from about the 19th to the 23rd of January (and in fact, one reference I found shows the Cusp of Aquarius for 1980 on Jan 20 at 21:49. I'd almost guarantee it would be possible to find others saying something else.)