Mary Murray Birth Record

Is anyone able to possibly find a birth record for my 2x great grandmother mary murray, she would of been born around 1873/1874 in co tyrone she married a william mulholland in inishown buncrana in 1897 he died in 1906 and from some of the info someone got me on here which thank you very much for she ended up in omagh co tyrone and remarried Francis Davidson in 1915 so something is telling me she must of been from around that area in co tyrone to go back there from buncrana, i’m kinda at a brick wall with her birth record i don’t know her mothers maiden name but some talk in the family they’ve heard of a McLaughlin name so maybe it’s possible that’s her maiden name? i haven’t found a marriage record for mary’s parents either, Michael Murray born around 1826 and Eliza/Liza as she’s went by on a census Eliza was also born in co tyrone according to a census, thank you very much