Hi Charlie,
I just pulled my records, which cover 56 pages of reports on wood and coconut fibres from Oak Island. One sample of coconut fibre from the museum was dated with 95% confirmation by Beta in 1993, to between 1168 and 1371. This is the one I have been referencing.
Wood, has been all over the place form 1025 to 1970, with a sample of Charcoal from 148bc.
There have been three other datings of the fibre, two by National Ocean Sciences, submitted by Woods Hole in 1996, and one other by Beta in 1990.
Cheers, Loki