Many McElderry descendants in the US (myself included) come from the Jonathan Webster McElderry line. The information on his parents and the immigrant ancestor is lacking. Jonathan was born abt. 1771 in Pennsylvania. He married a Margaret McCabe and they migrated west to Ohio where he died in 1848. Jonathan and Margaret had 12 children. He is my 3X great grandfather.
I have seen no hard evidence, but some folks believe that Jonathan's father was a John McElderry born abt 1720 in Ireland/N. Ireland and died in Pennsylvania abt 1785. Also, that John was married to a Ruth Webster who may have been born in Sheffield, Yorkshire, England abt 1726 or 27.
I would be very interested to know if your information on the McElderry family of Ballymoney provides any clues as to Jonathan's parentage.
Thank you very much!