Eliza Jane Webber was born in England, probably on 6 October 1835, the daughter of William Webber, a surgeon, and his wife, Eliza Preston. The precise place of her birth is unknown; it may have been Great Yarmouth, Norfolk. On 20 July 1869 at Spring Grove, Middlesex, she married William Garden Cowie, who had recently been consecrated bishop of Auckland, New Zealand. Arriving in Auckland on the City of Melbourne on 3 February 1870 with her husband, she resided at Bishopscourt in Parnell for the rest of her life. Eliza and William Cowie had one daughter and five sons, two of whom died in infancy.
Eliza Cowie became well known for her social and welfare work among the less fortunate in Auckland at a time when social services for women were almost nonexistent. In 1884 she founded and was superintendent of 'a retired and peaceful' women's home in Parnell set up 'to receive young women desirous to return to virtuous living.' The home provided shelter and the opportunity for single mothers (some as young as 15) to be reinstated into society 'without the ineradicable brand affixed'. They were expected to remain for six months, the intention being to change their living habits and to teach skills of sewing, laundry and household work.
Eliza Cowie also took a leading role in the work of the Auckland Ladies' Benevolent Society and as president of the Girls' Friendly Society. The children's home in Parnell (founded in 1893) and another in Ponsonby (1896) also owed their existence to her efforts. She was a member of the committee of the Mission to the Streets and Lanes, and of the ladies' committee of the Association of the Friends of the Blind, and also the first president of the Auckland Anglican Mothers' Union.
Taking a deep interest in her husband's work as bishop, Eliza Cowie entertained large numbers at Bishopscourt (up to 700 on one occasion). She travelled a good deal with the bishop in his visits to various parts of the diocese of Auckland, calling on the wives of clergy – both European and Māori – and travelling in unpleasant conditions over rough roads by horseback. She was said to be the first Pākehā woman to make the journey from Wellington to New Plymouth on horseback.
Around 1895 she suffered a stroke and was paralysed on one side. Confined to her home she continued to receive visitors. On 26 June 1902 Bishop Cowie died. Eliza Cowie remained at Bishopscourt until her own death on 18 August of the same year. She was buried in St Stephen's cemetery, Parnell.
The women's home (now known as St Mary's Family Centre) remains as her most enduring achievement. Her work with distressed women and children was significant in the context of that period in Auckland's history: she was indefatigable in her organisation of and fundraising for the women's and children's homes. She was described as 'one of those gentle Christian women whose loving deeds and good example can be ill-spared', and by Māori clergy as 'our mother, Mrs Cowie'.