Do you have any leads on names of possible children. There are too many name variant parent combinations on BDMNZ online to be certain. Margarets full name Margaret Mary Agnes Riley. There are no births with mother Margaret and father Joseph. However many mother Mary and father Joseph also mother Mary and father Patrick and others with Margaret - Patrick & John.
Papers mention Joseph's death, his father Williams death and Margarets payments of his debts 1888. Many references to Joseph as he was an undertaker.
Margaret is named as Executrix to the will of Peter Murphy 1887, a Greymouth Greengrocer. He appears to leave eveything to her. Maybe this is why she can pay off Josephs debt a year later??
Margaret may have remarried?? - A Margaret Mary Quinn marries Charles James Lawerence on
27 December 1894 BDMNZ 1894/3483. That said there seems to be a few Margaret Mary Quinns around NZ at the time.
Cheers - Séan