What I have been doing in the interim is research. I've ordered records from the Family History Library, as well as discovered that there is precisely one repository in New York City that is open at a time when I don't have to be at work, and that is the New York Public Library. And the New York Public Library holds the microfilmed Records of St. Peter's Church, and St. Peter's is where my great-great-grandmother was baptized! So off I headed after work on Tuesdays and Wednesdays, when the microfilm reading room is open late. (There's a chance another branch of my family entirely might have also interacted with St. Peter's Church, several decades later, but I haven't gotten to those records yet. I can't go tonight because sometimes the present has to take priority over the past, and we have no food in the house.)
I knew my 2x great-grandmother, Mary Ann Madigan, had been born c. 1868, so I started there and worked my way backwards through marriage records until I found the records of her parents, Mathew Madigan and Margaret Sullivan.
They were married 15 September 1867. Their witnesses were Simon Healy and Hanora Sullivan, who would later be the godparents of their eldest child. A Francis J. Healy was the witness to Mathew Madigan's naturalization several years later, and I'm really beginning to wonder who these Healys were. I've been told (but have no sources for the information) that Margaret Sullivan Madigan had a sister named Nora Sullivan Crowe. If that's true, Hanora Sullivan and Nora Sullivan Crowe are probably one and the same. I did notice that the priest's name was also Healy, so I e-mailed the diocese for information about the him. I got a brief bio in response. While I suppose there might be a relationship to the Simon and Francis Healy - who I don't yet know anything about - there's no immediately apparent connection to the Madigans.
Her sponsors were Simon Healy and Hanora Sullivan, just as at her parents' wedding.
I had a good guess for when Mary's younger brother James was born, so I continued forward through the records, and found James M. Madigan, born 1 September 1870, being baptized 4 September 1870:
His sponsors were Simon Cunningham (I have no idea who this is) and Catherine Sullivan. My information (I wish I had sources; instead I have "information") says that Margaret's two sisters were the aforementioned Nora, and Bridgett Sullivan Consodine. Two brother, Conn and James, are also mentioned. I suppose Catherine could be a sister-in-law, a cousin, or an otherwise unknown sister.
I continued working my way through the baptismal records, expecting to find the youngest sibling, Margaret, who was born c. 1873, represented as well, but I was unsuccessful. The question is to figure out why. Where were they?
In 1870, they were living in Manhattan, having James baptized at St. Peter's.
In 1872, they were living in Manhattan, with a NYC Directory putting them at 482 Canal Street, near enough to be attending St. Peter's, though it's not the closest of the Catholic Churches currently in existence in the neighborhood.
In c. 1873, Margaret was not baptized at St. Peter's in Manhattan.
In 1875, they are not listed in the NYS Census in Brooklyn, which suggests the possibility that they were still in Manhattan. (1875 NYS Census returns for Manhattan were lost.)
In 1876, when Mathew was naturalized, his address was given as 85 Luqaar Street, Brooklyn.
In 1880, the Madigans are enumerated at 85 Luquer Street, where they or their descendants would remain through at least 1940.
Sometime between 1872 and 1876, the Madigans moved to Brooklyn from Manhattan. It would seem that it happened after the 1875 NYS Census was enumerated, but if that's the case, where were they living when Margaret was born? Where was she baptized?