Most of the surviving baptism and marriage records for Dublin city parishes are available on the free IrishGenealogy website - the baptism you mentioned took place in the Roman Catholic parish of St. Nicholas (Francis Street), unfortunately there's no mother's maiden surname recorded to confirm a marriage. Can you post the details of that 1823 St. Nicholas marriage you mentioned - I'm not seeing an RC marriage with those names
The records for St. Nicholas RC go back to the 1740s but there are gaps, some sections that are very difficult to read, and also parts of of order .. possibly rebound incorrectly.
I dont see a likely marriage or any other children for Denis and Anne in St. Nicholas or wider Dublin city RC records, it's possible that they came from outside the city. Like many other large towns and cities there was a general drift of people to the city over the years, not just from county Dublin but all over Ireland and some from Britain. Connecting further back with any certainly would be difficult due the the lack of detail in early records.The date in this case is early for Catholic records, the average starting date for Catholic reguisters in rural areas is about 1830 , so if Denis and Anne originated in a county parish there may not be any written record available. Many early records are noted in Latin so Dionysius or similar for Denis.
for reference : Military records generally noted place of birth as the Civil parish, in this case in addition to the Catholic parish of St. Nicholas there were also two Church of Ireland parishes of St. Nicholas (within & without).