Thank you to those who pointed me in the direction of ScotlandsPeople, I didn’t even think of looking in that direction.

Unfortunately I did not get a hold of Maggie’s birth but I did get her marriage and some information about Patrick Green.
14th July 1905 at the RC Church Uddington, marriage of Maggie Rooney (18) and Patrick Docherty (28). Both of Newlands Row. Maggie dau of John and Ellen nee Conroy. Patrick son of James and Catherine nee Curran. Witnesses were William Keegan and Catherine Docherty.
Patrick Green born 15 Apr 1876 at 2.45AM at Pound Street, Baillieston. Parents Francis Green (miner) and Annie Dullen. Father Francis absent for birth.
I also managed to confirm my theory of Patrick’s father Francis having been killed in a mining accident.
Francis Green, miner, married to Ann Dillen. Dec 26 1905 at 2.15pm, Calderbank Colliery, aged 55. Parents Patrick and Catherine. Informant Patrick Green, son, of 15 Reids Row Baillieston. “While the deceased was walking into the cage at the pit a piece of coal accidentally fell down the shaft of the mine and struck him on the head.”