Didn't realise you already has Bridget's maiden name!

Here's another birth for the couple:

Ireland, Births and Baptisms, 1620-1911 Ireland, Births and Baptisms, 1620-1911
Name: Archer
Gender: Female
Birth Date: 27 Jan 1869
Birth Place: 2 North City, Dub, Ireland
Baptism Place: 2 North City, Dub, Ireland
Father's Name: David Archer
Mother's name: Bridget Madden
FHL Film Number: 101181

And possibly this too: (mother ELIZA MADDEN, but father/area correct)

Ireland, Births and Baptisms, 1620-1911 Ireland, Births and Baptisms, 1620-1911
Name: Archer
Gender: Female
Birth Date: 19 Jul 1871
Birth Place: 2 North City, Dub, Ireland
Baptism Place: 2 North City, Dub, Ireland
Father's Name: David Archer
Mother's name: Eliza Madden
FHL Film Number: 255827

Good luck.