The records of North Kingstown burned in the 1800s. Although it is possible the parents are Jonathan and Eunice, there were other Bly couples in the area at the time. We may never have a solid reconstruction of the names as there were at least fifty names partially or completely lost that may be associated with the Blys. Thirteen were definitely Blys, the rest do not have enough record left to know the surname.
One solid link is to Daniel Bly, probably out of Salem. He was in N. Kingstown in 1679 and had a daughter there. HIs other children and grandchildren are probably in the lost records. He also bought Bly's purchase in 1709, known as Swamptown.
If you have further records of the family from another known source, please let me know. I am working on those connections now.