I research the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800.
Note 1 - Without a KNOWN parish, the chance of an ancestor's rcds NOT being in this database is AT LEAST 35%.
Note 2 - Only 1/2 of Co. Cork's rcds are in this database.
Note 3 - The RC church kept control over most parish rcds from Tipperary (north). These are ONLY available thru the Tipperary Family History Research center at a substantial fee (regardless of outcome).
For Johanna Sullivan B 1856 +/- 1 yr somewhere in Ireland with a father forenamed Jeremiah, I found 4 rcds: 1855 CRK (Donoughmore parish), 1855 CRK (Carrigtwohill), 1855 LIM (Dromcolliher), 1856 CRK (Aghinagh).
For Mary Sullivan B 1854 ditto, I found 1 rcd in 1854 CRK (Coachford).
For David Sullivan B 1849 ditto, I found 1 rcd in 1848 LIM (Dromcolliher).
For Cath(erine) Kiely B 1821 +/- 2 yrs somewhere in Ireland with the father's forename unknown, I found 12 rcds - too many to list here
For Jeremiah Sullivan B 1816 ditto, I found 15 rcds.
For Cath(erine) Kiely M 1847 +/- 1 yr somewhere in Ireland, I foundrcds: 1846 LIM (Solohead & Oola), 1848 LIM (Kilfinnane) and 1848 CRK (Killeagh).
For Jeremiah Sullivan M ditto, I found 19 rcds: 1846 LIM, 1846 LIM, 1848 LIM and 1848 LIM and 15 in Co. Cork. None of these matched with those for Catherine at the parish level of detail.
Because of the inconsistent parishes, especially for the marriage, I conclude these are likely NOT for your ancestors. Their rcds, if they exist, are likely in the undigitized parts of either Cork, or Kerry. Suggest you wait until these rcds are added to the database.
Google the Foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.