welcome to rootschat, found some siblings of john richardson on familysearch.org
robert 17-2-1865. wm henry 24-5-1867. eliza ann 18-1-1870. sarah 17-4-1872. all born loughgall,armagh.
parents. wm.henry richardson & margaret elliott.
marriage of his parents. wm. henry richardson to margaret elliott age 21. 19-4-1860. @ annaghmore cofi,loughgall,armagh.fathers. wm richardson & archy elliott.
found two births for margaret jackson but can't be sure if any of them is yours.
margaret matilda jackson 21-3-1873 armagh parents john jackson & anna maria willis.
margaret anne jackson 24-9-1874 armagh parents john jackson & anne eliza wright.
regards mary.