Hello Lucy...
Just some further info. None of it verified, nor possibly of any use :-)
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The 22 Mar 1874 Margaret McGRATH baptism possibly relates to the following BDM NZ Births entry...
BDM NZ Births 1874/29131 - McGRATH, Margaret - mother: Margaret father:Patrick d.o.b 19 Mar 1874BDM NZ Search
https://www.bdmhistoricalrecords.dia.govt.nz/search/There is a Patrick McGRATH and a Margaret McGRATH buried in adjacent graves at Linwood Cemetery, Christchurch. Possibly the above mentioned father and mother. Or not.
Margaret McGRATH - d.o.d 28 July 1923 - Block 45, Plot 256 Linwood Cemetery
http://librarydata.christchurch.org.nz/Cemeteries/interment.asp?id=93739Patrick McGRATH - d.o.d 16 Nov 1927 - Block 45 Plot 257 Linwood Cemetery
http://librarydata.christchurch.org.nz/Cemeteries/interment.asp?id=97023There is a mention of Doyleston in Margaret's burial record. Lincoln is about twelve miles up the road so I'd guess that Doyleston is well within the Lincoln registration district..
EDIT:
PapersPast - Obituary of Patrick McGRATH
http://www.rootschat.com/links/0s2y/Possible probates
McGRATH Patrick- West Oxford & Christchurch - Widow - 1927
http://archway.archives.govt.nz/ViewFullItem.do?code=20183057MCGRATH Margaret (R23089583) - 1923 - 1923 Doyleston - Married woman
http://archway.archives.govt.nz/ViewFullItem.do?code=23089583-----
The only 1877 McGRATH birth in Rangiora that I could find was for Peter Stephen McGRATH.
BDM NZ Births 1877/4578 - McGRATH, Peter Stephen - mother: Margaret father: Peter d.o.b 8 Apr 1877
which corresponds to ....
BDM NZ Births Microfiche - 1877/1454- McGRATH, Peter Stephen - Rangiora - Q2April 1877 plus nine months gives January 1878 so the December 1877 baptism is more than likely not for a younger sibling to this Peter Stephen McGRATH.
Peter Stephen McGRATH died in late December 1946. His remains are in the Church of England Cemetery at Rookwood, Sydney, Australia so he's unlikely to be on the Catholic Diocese Baptism CD anyway. Or not.
Trove - 2 Jan 1947 - Page 16 The Sydney Morning Herald (bottom of third column)
http://nla.gov.au/nla.news-article18019131-----
The only other 1877 Christchurch birth for a McGRATH that I could find was the following...
BDM NZ Births 1877/13122 - McGRATH, Mary Margaret - mother: Kate father: James d.o.b 14 Aug 1877
which corresponds to ....
BDM NZ Births Microfiche - McGRATH, Mary Margaret - 1877/2561 - Christchurch - Q3She may have married Herbert SEWELL in 1912.
BDM NZ Marriages - 1912/8183 - Mary Margaret McGRATH to Herbert SEWELLAccording to her age at death and date of death Mary Margaret SEWELL was born c.1877
Timaru Cemetery
http://www.timaru.govt.nz/services/cemetery/plot/16820-----
Citing the December 1877 baptism record you wrote...
"McGRATH [alias TURNER] - Margaret" Is this the child's name or does this refer to the mother
"Mrs Peter McGRATH"Regards
Beg