I searched the Irish Family History Foundation's online database for the name Anderson in Co. Armagh. Rcds B4 1840 are sparse. There are 701 B rcds dating back to 1711 and 501 M rcds also dating to 1711.
There are 3 B rcds for Mary Ann Anderson in 1838 +/- 4 yrs. Google the Foundation's name to browse the database.