The petition to replace the sand soft fall pit at Lenham Park has been signed by 34 local residents and was presented to the council in March.
A report to council said the park was closed within 30 minutes of the City being notified a young child had been injured, with the sand raked by staff to about 60mm.
No other needles were found.
The playground remained closed until the following day, when the sand pit was sieved by a contractor and reopened.
It was upgraded through the City�s playground renewal program in 2012-13. An assessment at the time said sand was the better option because the park had �good passive surveillance surrounded by residential properties�.
�Previously routine maintenance had removed glass from the play area in 2012,� the report said.
The report recommends against installing rubber soft fall.
It said that the needle stick injury was an isolated incident and the park did not have a record of continued anti-social behaviour.
�However, it is appropriate that the City focuses on a strategy to monitor the park over the next 12 months through a range of maintenance and community safety strategies to determine any ongoing risk,� it said.
�Should it be determined as an ongoing risk, then consideration be given to the replacement of the sand soft fall.�
Councillor Domenic Zappa has asked for the council to be given a copy of the assessment as well as costs for installing rubber soft fall.