Rachel/Rachael died in 1935 and was buried at the Botany Cemetery with her husband Thomas BOWMAN. The burial record gives her age as 76 and this may be her birth:
6510/1859
CHO, RACHEL
CHARLES & ELIZABETH
at CARCOAR
There is no consecutive registration number for another child that might be a twin.
That birth certificate should give information about when and where Rachel's parents were married, and Charles occupation, their usual address, and details of Rachel's older siblings. In 1859, the Elizabeth COE who died Coonamble 1898 aged 77, was in her mid 30s.
so perhaps born in 1820s.
So I had some spare moments this afternoon, and I have let my fingers do the walking, online, and from my armchair only.
I notice the following submitted information which makes me suggest that much of the info on those links Tracey has given in the OP are off the mark or not giving all the info they have found on various documents. I share:
Elizabeth, who died July 5, 1898, Coonamble NSW is noted as the wife of Charles COE, at the following SUBMITTED family tree:
http://www.wikitree.com/wiki/McGuinness-118 So on that tree, Elizabeth 1806-1898 is also noted as the wife of Richard PEARCE, with their marriage as 9 January 1832, Scott’s Kirk, Margaret St, Sydney. And the citation for that marriage as V183222073A. That Elizabeth is given as the mother of Elizabeth PEARCE, born 21 Nov 1833, Richard PEARCE born 22 April 1834, Mary Ann PEARCE, born 9 April 1836, Robert PEARCE born 21 March 1838, Charles COE born about 1844, Berrimah, and Annie “Jane” PEARCE born 22 June 1844, West Bargo . The tree owner cites “A Convict Maid” as the source for the info re Annie “Jane” Pearce.
IF this turns out to be your Sophia’s ancestors, then my armchair searchings today lead me to comment that perhaps her mum may be one of the following lasses (A Convict Maid)
Elizabeth MACGINNIS on the Friendship of 1818 (wife of a Daniel as per her CF)
Elizabeth MCGEE on the Kains, 1831
Elizabeth KAYE (aka JONES) ON THE Kains 1831
Eliza COX on the Edward, 1829
BUT there’s so many many many dots between Sophia OSBORNE and Jane PEARCE that need to be checked and re-checked, official documents to be obtained, validating, eliminating and all those usual significant checks.
What I am surprised to see on any family tree with NSW families in the 1830s is a Presbyterian marriage and it followed by a C of E baptism for their first born.
I find that lass Elizabeth, as a daughter for Richard and Elizabeth and that lass was born 21 November 1832, (not 21 November 1833 that the submitted tree gives) Further I find she was baptised in January 1833. I have used two reliable sources (the historic records at family search and the NSW BDM Early Church Records "V" series)
https://familysearch.org/ark:/61903/1:1:XTC8-JQJhttps://familysearch.org/search/collection/location/1927080?region=AustraliaNSW BDM (INDEX only so not research, just look up searching)
Richard PEARCE and Elizabeth MCGUINNESS, marriage as Vol 73A, line 220, 1832. (JA code Scots Church, Presbyterian) (so matching the reference nos. on the submitted tree)
http://www.bdm.nsw.gov.au/Pages/family-history/early-church-codes.aspxand
Isabell daughter of Richard and Elizabeth PEARCE, Volume 17, line 410, 1833.
So, it seems to me that there's been various different people over the years try to prepare a family tree, and get themselves tangled up perhaps due to lack obtaining the official records.
JM