The competition regulations stipulate that all matches should be played on grass and Terenure were unable to provide a suitable venue for the original replay date on Friday May 24.
Terenure had secured a suitable Dublin venue for Sunday June 2, but this date was unsuitable for Donemana who have a scheduled fixture at Coleraine on that day.
A Cricket Ireland spokesman said: "The Cricket Committee notes that Terenure Cricket Club had made efforts to secure a grass pitch on which to play the refix of the tie on Sunday 2 June - these efforts are to be commended. The Committee would like to acknowledge the fact that communications between the two clubs on this issue have been conducted in a professional and respectful manner on both sides and we look forward to continuing good relationships between both clubs and Cricket Ireland as we move forward together in what is an exciting time for cricket in Ireland."
