Councillor Rick Curach said a lot of people reminisced about the old days but things had progressed since then.
He cited various Acts and council policies that protected Moturiki.
A report to the meeting said the petition from Mount resident Catherine Hunt did not contain any supporting information.
The report said Moturiki was a conservation zone and special ecological area in the council's City Plan, with outstanding natural features and landscape values.
Councillor Matt Cowley said there was no way the project would have got through an Environment Court appeal process if the council had supported the petition.
Councillor John Robson said the petition showed there was a lack of understanding in the community of the constraints on the council.
Someone had spent a lot of time and energy on the petition, with the community frustrated that the fun park was not a flyer on Moturiki.
"We need to get the community more informed about what is possible so they can put their energy into something with a reasonable chance of success," he said.
Moturiki (Leisure) Island history
* Originally a defended Maori pa with terraces visible until 1940
* Quarry established 1910 and closed 1926
* Quarry site leased out for Marineland Park in 1966
* Marineland replaced by Leisure Island in 1981
* Waterslide, bumper boats and hot and cold pools closed in 1990