I assume this family was RC. The baptisms, death, and marriage are all before the start of statutory registration in Ireland (1864) and so you have to rely on church records. Unfortunately many of the parishes in Fermanagh don’t have birth or marriage records for the years you are interested in.
I searched the Irish RC parish records on Ancestry but did not find either Rose Ann’s birth or her marriage. Few RC churches kept burial records so there’s unlikely to be any record of either Patrick Martin’s death if before 1864.
DNA resting may be the only way of identifying the right families.