The idea of the First Lady bearing a child during her husband's term in office today seems strange, almost indecent. Has such a thing ever occurred in American history?
If not, what might be the reason for the absence of presidential births? Is it simply a matter of the age of the typical First Lady, or is there any evidence, for example, that conceiving a child during one's presidency was or is culturally frowned upon?
Frances Folsom Cleveland had two children while her husband, Grover, occupied the White House, both of them in his second term. Daughter Esther (born in 1893) is the only baby of a president to be born in the White House, though there have been a number of kids born at 1600 Pennsylvania Avenue. The Clevelands had a second child, Marion, born while in office two years later.
The only other birth to a wife of a sitting president was to Jacqueline Bouvier Kennedy, who gave birth to a boy, Patrick, in 1963. Sadly, Patrick died 2 days after birth in Massachusetts.
Perhaps not what you're looking for but a little digging did also turn up Angelica van Buren, president Van Buren's daughter in law. She acted as first lady because Van Buren was a widower, and gave birth to a daughter in the white house, though the child died soon afterwards.
Emily Donelson, served as first lady for her uncle Jackson gave birth to three children in the white house. (http://www.firstladies.org/biographies/firstladies.aspx?biography=7)
As to why it's uncommon, well, take a look at this list of first ladies. The majority of them started their tenure in their 40s or even 50s, past the age most women (can) bear children. I'm curious though, why would it be indecent?