Families and children lobbied Woollahra Council for six years to build skate and basketball infrastructure in Rushcutters Bay Park for youngsters to shoot hoops and practice their kick-flips.

But an initial plan to use 2 per cent of the 5.3 hectare park, in a pocket of land beside the harbour and the park's canal, was staunchly opposed by some residents.

They feared the facility – which would cater to children aged eight to 14 – would be noisy, attract anti-social behaviour and destroy trees and green space.

Among them was Mr Turnbull, who took the rare step of writing to the then-Liberal-dominated council to argue the leafy, pet-friendly park was better-suited to outdoor sports and recreation.

He said in his letter to the council that "adding hard surfaces and concrete structures is not sympathetic to how the park is currently used by its visitors", and cited noise concerns.

The park, which is in Mr Turnbull's now up-for-grabs electorate of Wentworth but borders Elizabeth Bay in Ms Plibersek's seat of Sydney, is a favourite with joggers, dog walkers and sports players.

Ms Plibersek landed on the opposite side of the argument, voicing support in her letter to councillors and saying the park "lacks recreational facilities for older children and young people".

The council rejected that proposal in 2017.

But under a revised concept plan put forward by the council this year, the youth recreation area would instead be built on a site in the park's south-west corner beside New South Head Road.

It would include a basketball practice area, skate and scooter infrastructure.

The council says no trees will be destroyed and the plaza design will include landscaped areas.

The fresh concept design won unanimous support from the council's finance, community and services committee at a heated meeting attended by local families and opponents on Monday night.

Liberal councillor Anthony Marano, a long-time supporter of the skate park, said nearly 60 per cent of about 600 submissions the council received were favourable to the new plan.

"I think it's going to be an asset to our parks that we currently don't have."

But submissions from opponents of the project, which were among those published in a council committee report, continued to express alarm at the project.

A petition circulated by the Darling Point Society, which garnered 800 signatures, criticised the facilities' encroachment on grassed areas and said nearby Centennial Park was a more suitable site.

"We don't want any structures or activities to encourage drug peddlers to return to Rushcutters Bay Park," the petition read. "No 'youth facilities' here!"

Society president Charlotte Feldman said young people had a right to sporting facilities but she wanted the park's heritage and green space, including several nearby fig trees, protected.

"My reason for opposing the construction of a skateboard park is the huge loss of green space on the edge of our magnificent world-class harbour which, once lost, can never be replaced."

Cr Marano said council staff had previously met with Mr Turnbull's office about the revised proposal; neither Mr Turnbull or Ms Plibersek provided submissions to the council on the new plan.