Girl Rose,
Church registers filmed by the LDS end about that same time, so unfortunately I can't help with Margt birth, but you can do an on-line search of the index to see what comes up. I believe Rootchats has a link under Ireland-General, or maybe someone out there can help us with the link to Ireland births index. I really must do a better job at keeping those links handy myself. Sorry!
I also sent your request to a friend, she may some info that can help on the Moyles.
Here is the 1911 census results for moyles in Derreen:
First LAST RELATION AGE Birth ear OCCUP M,S,W YRS,# CO BIRTH
John Moyles Head 72 1839 m Mayo
Bridget Moyles Wife 68 1843 m 40/10/8 Mayo
Bridget Moyles Dtr 16 1895 s Mayo
Peter Moyles Son 14 1897 s Mayo
It appears had 6 other children that are still alive in 1911, so Margt could be one of them. I also did a search for a Margaret, and there were none in Crossmolina in 1911, so she may have gone to Scotland by then for work.
I found one entry for Terrence:
YEAR PAGE MONTH CHILD FATHER SURNAME MOTHER SURNAME RESIDENCE WITNESS WITNESS WITNESS WITNESS
1846 50 2-Sep John Terence Moyles Mary McDonnell South Carrowgarve martin McDonnell Ellen McGowan
I suggest you concider going to the North Mayo Genealogical website and sending an email to see if they can help. There records are more complete since they have cemetary records and all surrounding parishes too.
You can also do a search for Margt Moyles from this site as well I believe.
http://www.mayo.irish-roots.net/Centres.htmI'll let you know if I hear from my friend.