I search the IFHF's online database at 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 almost non-existant. Many B/M/D events either weren't recorded, or haven't survived.
For Jos(eph) Howard B 1828 +/- 5 yrs, somewhere in Ireland, with the parents' names unknown, I found 4 records: 1-1823, 2-1825, and 1-1828. The associated respective counties are Kildare, Cork, Limerick, and Antrim.
For Joha(nna) Short B 1830 +/- 2 yrs, ditto, I found 0 records. Short isn't a typical celtic Irish surname. Neither is Howard. This suggests they MAY have been protestants. Protestant records are far LESS likely to have survived.