It was called "Woodville" - Mother and Baby Home - 176 Raddlebarn Rd.
I have a document that states my grandmother nursed her newborn baby there(he was born in Dudley Rd. Hospital(and my mum). They had three months to decide what to do with their babies - of course in the 1940's and war all around, there was no family payment for single mothers so it was usually adoption.
All the young mums would walk down to St Edwards Church on the corner for the baby christenings and to go to Mass (I know this because my Dad felt embarrassed when I told him what had been discovered of the past - because the local boys would go and tease them as they walked into Church!).
Father Hudsons Homes at Coleshill administered everything. Nan was there in 1944, but I read that Phil Lynott of Thin Lizzy had a home there in 1949 and was christened at St. Edwards!