Hi Anne-Elaine,
Have you seen a web site - Sir John Rogerson - Turtle Bunbury? It is principally about Dublin Docklands but gives an overview of Sir John Rogerson's life.
He lived 1646-1724 married Elizabeth Proby.
His eldest son John (1676-1741) became Chief Justice of Ireland. He married Elizabeth Ludlow, had 5 children (4 girls) and the son John (1719-1785) is said to have died unmarried age 66.
I have not found any links nor can I find any of William Bell Rogerson children's births in Ireland (without possibly searching records for a fee). The only son born in England was George Nugent Ippersal Rogerson in Liverpool in 1846. A strange set of names, which could suggests some links to other families?
There is a suggestion that Sir John Rogerson's younger son was William Rogerson and that William's wife Alice (or Alicia Molyneux) remarried Sir Richard Wolseley after William's premature death. I wondered if a connection could be made from this line? Maybe there was a child from her marriage to William before she remarried?
Just some thoughts that may help. I will keep looking to see if anything crops up.
Alan