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.