Jane and Alexander seem to have settled in the South Island, and had seven children.
Mary Elizabeth Kennedy was the third child of Alec and Jane Kennedy, and was born in 1888. Mary was listed as a registered Barmaid in 1911. Mary Elizabeth never married and died on 4 September 1968.
The youngest Kennedy child was Alexander B Kennedy, who was born in Springfield, in 1896. Alexander died on 18 November 1920 and was buried in the Bromley Cemetery on Saturday, 20 November 1920 (Block No. 34; Plot No. 79). Alexander was aged 24 years, and his usual residence was at 70 Bealey Avenue, Christchurch. At the time of his death he was a labourer.
Alexander Snr died in Timaru on 5 September 1914. He was buried on 8 September 1914 at Timaru Cemetery. Although his own family had been Catholic, he was buried by a Presbyterian Minister, Rev. Cooper. According to his death certificate, Alexander was 65 years old at the time of his death and he had been in New Zealand for for 56 years, which also ties in with the family arriving in New Zealand in 1858.
At the time of his death, Alexander's widow Jane was listed as being aged 52 years, making her birth date around 1862 (I believe she was actually born around 1860). At the time of his death, Alexander had four sons aged 29, 24, 20 and 18 and three daughters aged 27, 26 and 22. Jane Kennedy, Alexander's widow died on 18 June 1938, aged 78, which puts her birth squarely at 1860, as I had thought.