Re birth circa 1850, Lislafferty, County Tyrone

Any help with locating the birth date of Joseph Patrick will be appreciated. His parents were William and Rebecca Patrick, evidently tenant famers, living about 1850 when Joseph was born at what is now known as 5 Lislafferty Road, Newtonstewart, County Tyrone. Joseph migrated to Rockhampton in Queensland, Australia, about 1873 and died of "Phthisis"  (Tuberculosis?) in November 1893. Probably the Patrick family attended the Ardstraw Presbyterian Church.