A large amount of graffiti has been discovered on various pieces of equipment in the play park, which was opened in May.
The vandalism has been reported to Police Scotland, with the Community Action Team asked to provide additional patrols in the area.
Mark Rowley, leader of the c ouncil, said: “As a council we have committed significant funds to deliver some fantastic play facilities across the region over a number of years, and to see them mistreated in such a way is appalling.
“These play parks should be a safe environment for our young people and it is absolutely unacceptable that a minority sp oil it for their community.
“If anyone has any information that could help I'd urge them to some forward.”
The play park, which was part of the council's £4.8m playparks and outdoor com munity spaces programme, was opened in May, when it was hailed by council convener David Parker as “an excellent community facility with play equipment for all ages and abilities”.
Anyone with information on the damage caused is asked to contact Police Scotland on 101, quoting incident 1136 of December 22.