I search the IFHF's online database @ ROOTSIRELAND.IE. It has abt 19 million B/M/D and other records for MOST Irish counties. Records before 1863 are increasingly sparse. By 1800, they are nearly non-existant.
For Bridget Kenny B 1856 +/- 5 yrs, somewhere in Ireland, with a father forenamed Francis, I found 1 record: 1860, Co. Sligo. However, the mother's names aren't either Kat(herine), or Phares.
For Francis Kenny B 1835 +/- 5 yrs, ditto, with the parents' names unknown, I found 19 records, but NONE in Co. Wexford.
For a Kenny/Phares marriage 1850 +/- 5 yrs, ditto, I found 0 records.