I have had a good look for your William John Moore. There is a birth registered in Newtownards for a William in 1882 April/June quarter, Vol 1 page 842
which MIGHT be him, but I can find no record of a marriage between Samuel Moore and Jane Lightbody. There are lots of Samuel Moores in the Newtownards area and also quite a few Lightbodys, but without any further clues we can't go any further. It might be worth getting the details of this birth.
Do you know when William went to New Jersey??
RosemaryJoan