I spoke to Dad and he remembers both the Dempseys and the O'Conners and also your Dad, Jack Keegan selling vegetables.
First off in Number 10 the O'Connors lived in the right part of the building and the Dempseys lived in to the left. He thinks there were three O'Connor children:
Maire (pronounced Moira or Maura people christened Mary were often called this)
Larry (he thinks this was the name but all he remembers is something about him having a pair of roller skates as he would have been a bit older)
Patricia was the youngest and he thinks she was born in the mid 1930's so was a similar age to him.
He remembers old Mrs Dempsey who wore a turban (he thinks she had alopecia or similar) and her son Joseph but doesn't think there were any other kids and didn't know him well.
In terms of Jack Keegan he says he thought he was the father of the Dodder View Keegan family that I mentioned the other day. Dodder View is literally around the corner from Ballsbridge Avenue. All the kids were older than my dad who was born in 1936 but he does remember Peadar/Peter as being the youngest, probably born in 1935. He says there was definitely quite a few sons in the house and they had to build a shed out the back where they all slept. He remembers Peadar as a big, strapping lad who left to join the RAF when he was about 17 so you may be able to follow that up in the UK Military archives in Kew?
Also I forgot to add in my e-mail both Peadar Keegan and Patricia O'Connor were the image of each other with roaring red hair which may (vaguely) back up that they might have been cousins.
In terms of burials, I don't know generally, but any of our family from the area are buried in Deansgrange one of the larger cemeteries in South Dublin.
Again, best of luck with the search,