Do you know if James and Sarah were Roman Catholic or Protestant?
Civil Registration for Catholic BMD began in 1845 for Protestants and in 1864 for Catholics.
You will probably need to investigate church baptismal registers. If you can pinpoint where in Tyrone they were born, the list of Church Records from PRONI may be helpful. http://www.proni.gov.uk/guide_to_church_records.pdf
More Irish records are being digitized - I'm hoping to find more of my Northern Ireland family when that happens. http://www.irishtimes.com/business/sectors/technology/librar...