We probably can't help you without having some idea of dates.
Would Patrick have been born before or after the start of civil registration of births in 1864? If after 1864, do you have a copy of his birth certificate? If before 1864, have you searched for church records?
County Down covers a large area so you also probably beed to know where in Co. Down they lived so do let us know more and someone might be able to post information or suggest where you can search next.
