Green MP Marama Davidson appears to be the frontrunner to replace Metiria Turei as the party's co-leader when the votes are counted tomorrow.

But if it was up to the Greens' coalition partners, there is a general preference within NZ First and Labour for the other candidate, Julie-Anne Genter, to triumph.

The coalition partners have been impressed with how Genter has performed as a minister, and see her as less of a risk than Davidson to the Labour-led Government.

Some within Labour and NZ First were concerned that the three-party coalition was already vulnerable to being called disjointed, and that the more unpredictable Davidson would be more likely to create instability.

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Davidson has campaigned on her ability to criticise Labour more openly because unlike Genter she is not a minister. That could even extend to attending rallies in protest against the Government. She singles out a moratorium on deep sea oil exploration and fracking as one area she would take Labour to task over.

Genter has also said it would be crucial for the Greens to have an independent voice in Parliament if it was to survive, though she has promised not to criticise Labour in her portfolio areas – health, women's affairs and transport.

Davidson, who previously worked at the Human Rights Commission and on domestic violence issues, is believed to have slightly more support than Genter in the co-leader race, which is voted on by party members. But the Green membership have made surprise decisions before, picking rookie James Shaw as co-leader in 2015 and non-MP Russel Norman in 2006.

Davidson's Maori heritage and activist background appeal to the party's base, and she would complement the more centrist, business-friendly Shaw. She is seen as a natural replacement for Turei, who quit as co-leader in August after admitting to defrauding Work and Income while on a benefit 20 years ago.

"Obviously there are some similarities, and I'm very proud of [Turei] being the reason I'm in politics," Davidson said.

"But I'm also my own woman. I have a different activist background and will be bringing a whole different style of leadership to the Green Party if I am elected."

Green sources downplayed concerns about Davidson being a rogue member of the coalition. There were limits to how much she could shake up the Green Party, they said.

The Greens agreed with Labour during coalition negotiations last year that the new co-leader could not be used as an excuse to renegotiate their agreement or any policies.

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Both Davidson and Genter say they oppose the Labour-Greens' fiscal rules, which set strict limits for debt reduction and spending and were used to calm fears about the two parties' economic credentials during the election campaign.

"If you look at what we need to change to truly address the social, environmental and economic system we are operating in, we can't be putting up arbitrary measures on GDP, spending and Crown debt," Davidson said.

But she would not go as far as insisting that they be scrapped at the next election.

"I would be happy to open up the discussion for the caucus and the party, and work with James on that."

Out of the two co-leader candidates, Genter has been the more successful campaigner. She is also seen as having broader appeal beyond the Green Party, similarly to Shaw.

Genter won 15 per cent of the vote for the Greens in the Mt Albert electorate at the general election while competing against highly popular Labour leader Jacinda Ardern, well above the Greens' overall result of 6.3 per cent. Davidson won 7.2 per cent of the party vote in Tamaki Makaurau.

Some within Labour and NZ First were concerned that the three-party coalition was already vulnerable to being called disjointed, and that the more unpredictable Davidson would be more likely to create instability.

Davidson has campaigned on her ability to criticise Labour more openly because unlike Genter she is not a minister. That could even extend to attending rallies in protest against the Government. She singles out a moratorium on deep-sea oil exploration and fracking as one area she would take Labour to task over.

Genter has also said it would be crucial for the Greens to have an independent voice in Parliament if it was to survive, though she has promised not to criticise Labour in her portfolio areas – health, women's affairs and transport.

Davidson, who previously worked at the Human Rights Commission and on domestic violence issues, is believed to have slightly more support than Genter in the co-leader race, which is voted on by party members. But the Greens membership have made surprise decisions before, picking rookie James Shaw as co-leader in 2015 and non-MP Russel Norman in 2006.

Davidson's Maori heritage and activist background appeal to the party's base, and she would complement the more centrist, business-friendly Shaw. She is seen as a natural replacement for Turei, who quit as co-leader in August after admitting to defrauding Work and Income while on a benefit 20 years ago.

"Obviously there are some similarities, and I'm very proud of being the reason I'm in politics," Davidson said.

"But I'm also my own woman. I have a different activist background and will be bringing a whole different style of leadership to the Green Party if I am elected."

Green sources downplayed concerns about Davidson being a rogue member of the coalition. There were limits to how much she could shake up the Green Party, they said.

The Greens agreed with Labour during coalition negotiations last year that the new co-leader could not be used as an excuse to renegotiate their agreement or any policies.

Both Davidson and Genter say they oppose the Labour-Greens' fiscal rules, which set strict limits for debt reduction and spending and were used to calm fears about the two parties' economic credentials during the election campaign.

"If you look at what we are need to change to truly address the social, environmental and economic system we are operating in, we can't be putting up arbitrary measures on GDP, spending and Crown debt," Davidson said.

But she would not go as far as insisting that they be scrapped at the next election.

"I would be happy to open up the discussion for the caucus and the party, and work with James on that."

Out of the two co-leader candidates, Genter has been the more successful campaigner. She is also seen as having broader appeal beyond the Green Party, similarly to Shaw.

Genter won 15 per cent of the vote for the Greens in the Mt Albert electorate at the general election while competing against highly popular Labour leader Jacinda Ardern, well above the Greens' overall result of 6.3 per cent. Davidson won 7.2 per cent of the party vote in Tamaki Makaurau.