There are several institutions in New Zealand that have courses available. Unfortunately these courses are not known widely outside of New Zealand. Alternatively check out New Zealand Society of Translators and Interpreters(external link) website for courses available in New Zealand.
The National Accreditation Authority of Translators & Interpreters - Australia is a world wide recognised qualification. They have online courses available, as well as running exams in New Zealand. This qualification would allow you to work for other countries other than New Zealand.
To work for Language Line you need to have a formal qualification in interpreting. The Office of Ethnic Communities, do not employ interpreters directly. Serco Group - Language Services provide us with the interpreters.
Please email Serco if you want to be a Language Line interpreter firstname.lastname@example.org