The used needle was found near Park primary school, during the annual litter-pick in the area.
They were discovered by a local warden and community engagement worker.
Police said the discovery was “very concerning”.
They said the needle and syringe were found in an area were children regularly play.
Community safety Constable Siobhan Pellet said: “We would like to ask those people who do use needles to take care using them and to make sure that they dispose of them safely and in the appropriate manner.
“It is totally unacceptable that they are left lying where children can find them. The dangers of injury and infection through needle stick injuries are horrendous.
“It must be reiterated that if you see a needle or syringe lying in the street do not touch it but report it so it can be safely removed.”