The body of the 62-year-old former police officer was found in his flat at Sandy Braes on Monday, October 18, and police launched a murder investigation.
A funeral service for Mr Coulter will be held in Garvin's Funeral Home at Ballyronan Road in Magherafelt at 1pm on Monday, November 1, followed by burial in St Swithin's Parish Churchyard.
A notice on Garvin's website describes Mr Coulter as a "son of the late Olive and Joe, dearest brother of Belinda, brother-in-law of Trevor and father of Karen and the late baby Gillian."
It adds: "Sadly missed and always remembered. The day thou gavest, Lord is ended”.
On Monday, Sebastian Adrian Nowak (27), of Colvil Street in Belfast, was charged with murdering Mr Coulter on a date between October 13-18.
He was remanded in custody to appear by video link at Magherafelt Magistrates Court on November 17.
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