Name, month and year of birth (August 1870), date of death from Graeme Kenyon, whose great grandfather was James George Kenyon b.1861 (whose second wife was Ada Oliver b.1864, daughter of Samuel Oliver b.1833) quotes the Taranaki Herald of 1 October 1870:
“OLIVER.-On the 26th September, of erysipela, FRANCIS JAMES, son of Mr. F. Oliver, aged 7 weeks”.

Result from birth search on New Zealand BDM website in October 2018:
1870/18666. Oliver, Francis James. Mother: Elizabeth Ann. Father: Francis

Full date of birth of 7 August 1870 from further searching in October 2018 on BDM Search by incrementally changing the date range for the birth.

Result from death search on New Zealand BDM website in October 2018:
1870/7942. Oliver, Francis James died age 7W [Weeks of life matches]

Full date of death of 26 September 1870 confirmed from further searching in October 2018 on BDM Search by incrementally changing the date range for the death.