Hi
So far, I don't see a Margaret Mary Davies birth registration (1909-1910) on either the Eng & Wales GRO index or the North Wales BMD in the Llanrwst RD or other close RDs. There are quite a few Margaret Davies over the two years and a Margaret Ann Davies, Llanrwst 1909 but no Margaret Mary, so it's difficult.
There is a Margaret M registered in Llanrhaeadr yng Nghinmeirch in 1910 on the North Wales BMD. The GRO index has this as Dec q, 1910, Ruthin RD. It could be but Llanrhaeadr Y N is a way from Llanrwst. It is possible that Catherine got her granddaughter's birth place wrong.
Nothing is showing on the Family Search baptisms so it's not likely that FindMyPast has one either.
On the 1901 at RG13/5243/66/6 Bryn Rodyn, Trefriw, there are three daughters and one son who could be Margaret's parent:
Owen Davies, hd, 42, wheelwright, bGlan Conway
Catherine Davies, w, 44,b. Eglwysbach
Hugh Davies, s, 18, wheelwright, b. Glan Conway
Mary C Davies, d, 16, b. Llanrwst
Elizabeth E Davies, 13, b. Trefriw
Jane A Davies, d, 11, b. do
and the younger children
It might be worth you following up these 4 to see if there are any clues.
Sorry but my internet connection is very slow so it's taking a long time to just do one simple search.
Gadget