Jane was 2nd wife of Thomas Lecky Conyngham. They had four children:
henry 1843
John 1845
Elizabeth 1849
Rebecca 1852
After the death of her husband, Jane with her son John and two daughters decided to immigrate to NZ. They arrived in Auckland on 17th Aug 1878.
Fact: Burial Auckland, Auckland, New Zealand
Sources
"New Zealand, Civil Records Indexes, 1800-1966," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:QG6K-Y7SW : 4 January 2018), Jane Cunningham Aka Conyngham, 1913; citing Death, New Zealand, registration number 1913/328, Archives of New Zealand, Wellington.