Ms Ngapoe has the support of councillors Henare O'Keefe and Jacoby Poulain, who both said it was a great example of local leadership.
"We need more mums like this standing up for the community and looking out for the kids," Ms Poulain said.
Mayor Lawrence Yule said he had a great deal of sympathy with making small local parks.
"We'll ask officers to look at that but - we can't build a park in every street, so it is a bit of a balance," he said.
In their response to the submission the officers said they understood the push for a playground but given its location and limited accessibility, and one nearby at Len Harlen Park, it would not be a recommended site.
But Ms Ngapoe said her neighbours did not want to send their kids elsewhere, because they didn't know if they would be safe.
The officers said there was also no funding available for the location. "So any desire to develop a playground would necessitate a change in priorities," the officers reported, adding $60,000 would be needed for such a playscape.
While not wanting to speak for councillors before a decision was made on the submission, Mr Yule said green areas such as Kilkee Terrace Reserve had been set aside for future use.
"So they could actually be made available for a park [and] so it t is a logical play to want to put a park and some play equipment," he said.
Mr Yule said the council would have to work out where the priorities for funding were to see if they accommodate Ms Ngapoe's request. A decision will be made by the council on Tuesday.