Searching irishgenealogy.ie for Daniel Sullivan births in Mallow there are 48 results from 1868 to 1917. I opened all births from 1868 to 1898 but found no births to mother Mary Fitzpatrick.
THere are no marriages for David Sullivan to Mary Fitzpatrick on irishgenealogy.ie in any county so they probably married before civil reg began circa 1865. There is a marriage of Denis Sullivan to Mary Fitzpatrick in 1875 plus other Sullivan/Fitzpatrick unions in Caherciveen. familysearch.org has a christening of Daniel SUllivan 20 Jun 1847 to parents Daniel Sullivan and Mary Fitzpatrick in Boherbue, Cork, which is near Kanturk. Not too far west from Mallow.
Do you have any dates beyond 1820 for your family? To whom was Daniel Sullivan married? His father should be on marriage civil reg. Often priest handwriting Daniel and a David appear quite similar. Consider searching both names.
Other links: http://www.askaboutireland.ie/griffith-valuation/ http://www.census.nationalarchives.ie Catholic registers: http://registers.nli.ie