Name from the Headstones Records for the Buffalo Coromandel Cemetery found in July 2025:
200 In loving memory of EMMA beloved wife of R. FRASER, died 12 June 1939 aged 71 years. Forever with the Lord.
And beloved mother of JAMES died aged 9 years;
ELSE MAY drowned aged 2 years.
201 2/3643 Pte R.L.H. FRASER, Auckland Regt, died 20 August 1920 aged 27. [Son of Emma and Robert]
202 26/824 Rm W.H. JONES, Rifle Brigade, died 23 August 1940.

No record of birth could be found on the New Zealand BDM website as at July 2025.

Possible birth record in Sydney for our James Fraser? Did Robert and Emma/Emily go to Sydney after their marriage to visit his parents/grandparents?
Initial of “L” for second given name, year and place of birth, establishment of date through incrementally changing the date range for the birth from a search on NSW BDM website in July 2025:
Name: FRASER, JAMES L
Registration number: 25926/1891
Father's Given name(s): ROBERT L
Mother's Given name(s): EMILY
District: NEWTOWN [Sydney]
Date: 28 July 1891

Transcription of Australian Birth Registration for James received 15 July 2025 from Marilyn Rowan at GeniCert.
It records James second given name as “Lyle”. Interestingly, his place of birth in Auckland New Zealand but registered in Newtown Sydney on 31 August 1891. Did parents Robert and Emily (Emma) Fraser visit Sydney a month after James was born and, found the baby needed a registration upon arrival in the August. Father Robert’s place of birth is given here as Clunes, Victoria, Australia. The marriage certificate had stated Sydney? Anyway, here is the text of the registration:
REG# 1891/25926
Name: JAMES LYLE FRASER
Sex of Child: MALE
Date of Birth: 28 JUL 1891
Place of Birth: UPPER QUEEN STREET AUCKLAND, NEW ZEALAND (SEE NOTE**)
Father's Name: ROBERT LYLE FRASER
Father's Occupation: GOLD MINER
Father's Birthplace: CLUNES, VICTORIA
Father's Age: 25
Date of Marriage: 12 JUL 1890
Place of Marriage: AUCKLAND, NEW ZEALAND
Previous Issue: NONE
Mother's Name: EMILY JONES
Mother's Birthplace: AUCKLAND, NEW ZEALAND
Mother's Age: 22
Informant: ROBERT LYLE FRASER, FATHER, 72 O'CONNELL STREET NEWTOWN
Present at Birth: MRS KILGOUR, MRS JONES
Registered: 31 AUG 1891 - NEWTOWN
Notes: **TRANSCRIBER'S NOTE: CHILD'S PLACE OF BIRTH IS CLEARLY RECORDED AS
"UPPER QUEEN STREET AUCKLAND, NEW ZEALAND" IN THIS REGISTER

In the transcript, Mrs Jones is likely to be Emma’s mother, and Mrs Gilmour may have attended to the birth. According to newspaper reports in PapersPast, there was a Dr Kilgour and Mrs Kilgour who lived in Thames and retired in 1890 to Auckland.

Date and place of death, estimated year of birth of “1891” matches above record, from newspaper death notice published in the Auckland Star dated 18 Oct 1901:
FRASER. - ... Also, on September 12, 1901, at his parents' residence, Driving Creek, Coromandel, James, eldest son of Robert and Emma Fraser, after a long and painful illness; aged 10 years; deely [deeply] regretted.

Second given name of “McIntyre”, year and country of death, from death search on New Zealand BDM website in July 2025:
1901/3790. Fraser, James McIntyre. Died age 10Y

Full date of death of 10 September 1901 from further searching in July 2025 on BDM Search by incrementally changing the date range for the death.

Obituary of Elsie and James from the Auckland Star newspaper of 18 October 1901 found on the Papers Past website in July 2025:
FRASER. - On July 29, 1901 at Driving Creek, Coromandel, Elsie May, only and dearly beloved daughter of Robert and Emma Fraser, aged 2 years. Accidentally drowned. Also, on September 12, 1901, at his parents' residence, Driving Creek, Coromandel, James, eldest son of Robert and Emma Fraser, after a long and painful illness; aged 10 years; deely [deeply] regretted.
{NOTE: This Newspaper Notice gives date of death as 12 September 1910].