The most recent thefts occurred on Thursday, February 11 at 4pm and at 11am the next day.
Police are appealing for anyone with information to come forward.
Inspector Derek Easton said: “We are keen to hear from anyone who saw anyone acting suspiciously around the time of the theft.
“Although the turf was only worth around £40, we are treating it as a serious matter given the location of the crime and the lack of respect shown for those buried in the cemetery.”
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Anyone with information can contact police on 101 or Crimestoppers on 0800 555 111.