First, thank you for your kind and quick help! (I am a Dutchman, trying to piece together the ancestry of my British daughter-in-law; not easy.)
I now understand that I attributed the children I mentioned to the wrong John Dempsey. Thank you for finding the real parents of those poor children. I got confused because this couple was/is the only John Dempsey married to an Eliza(beth) I could find in the census of 1901 and 1911. I was fortified in my wrong path because I had found the death of an Elizabeth Dempsey in 1908, and the 1901 census had the couple while the 1911 census shows John Dempsey a widower.
Now knowing that I was on the wrong path, I looked again and found in the 1901 census
http://www.census.nationalarchives.ie/pages/1901/Queen_s_Co_/Mountmellick_Rural/Avoley/1650174/ an Elizabeth Dempsey as a widow with two children. However, I so far failed to find the birth certificates of the two children mentioned there, so I do not yet know of this is "my" Elizabeth Dempsey née Reilly. And although the John Dempsey on the last line of
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1898/05820/4647953.pdf seems a possible candidate for his death, the name of his widow is not given, so I cannot be certain that this is "my" John Dempsey. (You see that I am more careful now, thanks to your advice.)
If anyone is able to help me further to find the correct couple, I would be very glad.
Two minor remarks:
-I did not know how to add the links to the census or birth records, and had to ask someone more knowledgeable to explain this (hope the links above work!).
-I do not understand Sinann's remark: "This is the birth of Thomas Dempsey 24 Dec 1891, scratch that his birth is 24 Oct 1891 so his sister Anne 4 July 1887"
Thanks again,
Nicolaas
