The church last month asked its parishioners to donate the cost of a cup of coffee each week towards retaining a bishop, after the Rt Rev Dr Kelvin Wright announced his intention to retire at Easter next year.
When his retirement was announced, Dr Wright questioned whether the diocese could afford a bishop in future.
The church has never had a trust fund for a bishop's stipend.
By the end of last week, 21 people had answered the church's call, and raised $1088 towards a stipend for a bishop over the next five years.
Once promised weekly, fortnightly and monthly contributions were added up over a 12-month period the donations would total $5400.
But Vicar-general Alec Clark yesterday said the diocese needed about $50,000 a year to cover the shortfall.
``We're always grateful for whatever help people can give to us.
``We want to be respectful of the other needs people have in their lives as well.
``So we don't want to be inviting people who can't afford it to support us in this particular fashion.''
He said as well as the fundraising, the diocese was ``considering multiple ways'' to deal with the problem.