The two were found guilty at their trial in December 2010 of assaulting then 18-year-old Joshua Hart.
Mr Hart had been drinking with up to 50 young people in a park when police were called to break up the party and send them home.
Mr Hart was abusive to police after his drink was knocked out of his hands by Mr Needham.
Needham struck Mr Hart twice as he brought him to the ground and handcuffed him.
Mr Hart was then led in handcuffs to a spot in the park where other police officers were waiting, including Douglas.
Douglas was found guilty of striking Mr Hart twice in the face while the teen was handcuffed.
The two police officers had applied for a discharge without conviction after a restorative justice hearing with Mr Hart, who did not oppose the discharge.
However, Judge Allison Sinclair declined the application.
She found that the consequences of a conviction would not be out of all proportion to the offending.
Judge Sinclair told Douglas that while the offending was at the lower end of the scale, "it was a gratuitous use of violence on someone that was handcuffed at the time during the course of Mr Douglas carrying out his duties as a police officer."
Judge Sinclair fined Douglas $600 but did not fine Needham.
"As a police officer, I accept an entry of a conviction is a significant penalty in itself."
Needham has also featured in the news when he gave evidence at the Aisling Symes inquest in June last year.
He was one of the first police officers on the scene when two-year-old Aisling was reported missing in October, 2009.
Needham had found a manhole slightly ajar and checked the manhole but saw no sign of Aisling.
He did not tell his superiors about finding the manhole cover ajar, and seven days later Aisling was found 36 metres down the stormwater pipe.
