I have done some research on your query. The nearest matchup I could find is the marriage of Denis Sullivan, Ardcahan to Catherine Collins, Ardcahan on 17th February 1824. Witnesses: James Kehelly and John Collins
The children born to this marriage were:
24th Dec 1824 Ellen to Denis Sullivan & Cath Collins now living in Rea (a town land adjacent to Ardcahan)
1st April 1829 Catherine to Denis Sullivan & Cath Collins, Rea
23rd June 1833 Timothy to Denis Sullivan & Cath Collions, Knockahaghduv (another townland adjacent to Ardcahan)
11th March 1836 Denis to Denis Sullivan & Cath Collins, Knockahaghduv
16th February 1840 Denis to Denis Sullivan & Cath Collins, Knockahaghduv
This information I got from: http://churchrecords.irishgenealogy.ie
You will note two Denis' born to this marriage. I presume that the first Denis died in infancy, and it was usual that the parents named the next boy Denis again. I failed to find any baptism record for Patrick or John. It is possible that they were born in another parish besides Dunmanway. I found two daughters - Ellen and Catherine - you mentioned only one - Catherine
You mentioned Timothy's date of birth as March 1835 - the best I could find was 23rd June 1833. I wonder is this correct; maybe you could check your source for his date of birth
In the Tithe Applotments for the parish of Fanlobbus (now Dunmanway) -
http://www.corkgen.org/publicgenealogy/cork/titheapplot/fanlobbus/tithe… -
I failed to find any Denis Sullivan in any of the above named townlands; possibly he was a labourer and was not in possession of land at that time.
Griffith's Valuations of 1852 -
http://www.askaboutireland.ie/griffith-valuation -
shows no Denis Sullivan in this locality; possibly the entire family emigrated during the famine of 1845-49.
In another record of parishioners during the period 1832 to about 1846 I find the following:
Denis Sullivan, (Major), Knockahaghduv, labourer
Timothy Sullivan (Major), Rea
The agnomen 'Major' I understand to be a family nickname used to distinguish this family from other Sullivan families in the same locality. I mention this so that in your family research you may find reference to the term 'Major'; it may throw some light on the family lineage.
I hope this bit of information will be of help to you. If you have any further information that could throw some light on the subject please come back to me and I will do my best to help.
Yours
Tommy Collins
Dunmanway