Greetings, Manaia
I'm afraid I know nothing more about Eunité, just that she was George Burnett Stallworthy's nurse for the first ten years of his life.
His father, Rev George the missionary, left England in 1833 arriving at Tahiti in 1834. He was originally appointed to the Marquesas Islands and lived there for 7 years until that LMS mission was abandoned in 1841 - for three of those years he had struggled on alone amongst the
very cannibalistic inhabitants. He went back to Tahiti for a short period before being appointed to Fale'alili in 1842.
George married Charlotte Wilson in February 1844, and George Burnett Stallworthy was born 30 Dec 1844 which is presumably when Eunité's services were first required. (Charlotte died of consumption/TB in August 1845.)
Rev George married Mary Ann Darling in October 1847 at the LMS chapel in Apia. They went on to have nine children - eight born at Fale'alili (one died as an infant), the last one was born at Malua.
At the age of 10, George Burnett was sent to England for his schooling in December 1854. By then he had five half-siblings, so I would imagine that Eunité was still being kept busy.
In January 1859, the Stallworthy family moved across the island to Malua where Rev George became the principal of the Theological College, standing in for Rev Turner who was on leave. I have no idea if Eunité went with them or stayed in Fale'alili.
Rev George died 7 November 1859 at Malua. Mary Ann and the children left Samoa on the missionary ship
John Williams in January 1860 to go to England.
Rev David Darling (and his daughter Eliza) had left Tahiti in 1859 and gone to live at Parramatta, Sydney. He died there in 1867. Eliza went to England and lived with the Stallworthys in Kent until her death in 1899. I only know what Christine wrote on the RootsWeb board about Adam and Jemima Darling, and the only reference I've found to William Beddoes is a brief mention of him buying two small Fijian islands in 1869 - Nanuya Levu and Nanuya Lailai. (
http://www.turtlefiji.com/legend/history.php)
I wish I could be of more help.
Best regards
Koromo

PS. 'Koromo' is a nickname, and yes it is Japanese for a variety of ornamental fish (koi carp). However, I am a NZer although not living there.