One (or both) of you may already be aware of them, but there are records for what appears to be your Jeremiah Donovan in the Family Search database [https://www.familysearch.org]. ; If you create a (free) account there, you can find Jeremiah under ID number GQR6-TM1, and can access the records for the others easily through that record, as you will see. Jeremiah is shown as being born in Ireland, but later being married and dying in Nova Scotia. He and his wife, Elizabeth Robinson, are shown with 10 children, and the names are almost exactly what you gave (one or two are different).
The record for Jeremiah shows him as being born in 1785, and shows Patrick Donovan (christened 14 March 1761) and Jane "Checkley" (which may be a mis-transcription of Coakley) as his parents. There is a document attached to Patrick's record showing that he and Jane were married in 1823 in Ross, County Cork, which does not make sense under the corcumstances. Perhaps that Patrick was actually a brother who stayed in Ireland and married there. Jeremiah's record also shows Cornelius and Ellen Donovan as alternate parents, with no documents attached to evidence that, so some things are obviously wrong there. In each record, at the right hand side of the record you can see the screen names of those who have created or modified the record, and can send them private messages, so you might be able to get more info by contacting them to compare notes (and perhaps also locate some relatives that way).
FamilySearch is operated by the LDS church, and is free to use. You have to create an account to use it, but they don’t ask for much personal info, and no missionaries will contact you or anything like that. The database, which is the largest in the world (bigger than Ancestry) does not have separate family trees, and is essentially one huge tree of linked records, in which there is a single record for each person, with a unique identification number (although sometimes people unknowingly create duplicate records for the same person, which you can merge when you spot them).
As you may already have learned, some (but not all) parish priests, when writing down baptismal or marriage records, converted Irish given names to what they considered "Latinized" forms, or replaced them with Biblical names. At the time in question, nearly everyone in Cork spoke Irish (and most would have spoken little or no English), so your ancestor was most likely named Diarmuid (Dermot), a name which was often "anglicized" as Jeremiah (later shortened to Jerry in some cases).
In case Ross turns out to be the right place, at this link you can see a list of townlands in the civil parish of Ross, with links to info about each townland, Note that civil parishes do not always have the same boundares (or even the same names) as the Catholic parishes.
https://www.townlands.ie/cork/ross/
The Catholic parish is called Roscarberry, and is somewhat larger than the civil parish. Here's a link to the online records which are available for that parish. They only go back to 1814, so presumably you won't find any records for Jeremiah there, but you may be able to figure out where Patrick and Jane lived (assuming that they are relevant) from their marriage record (looking in or around 1823), since it may state the townland where they lived.
https://registers.nli.ie/parishes/0093
The Coakley surname exists almost only in Cork, and is an anglicization of the Irish name Mac Caochlaoich ("son/descendant of the bllind hero"). It was also anglicized as McKehilly, but that name appears to have been replaced by Coakley, except in Dunmanway parish, which is not far from Roscarberry. The Irish form of Donovan is Ó Donnabháin (the meaning of which is now obscure, although the donn part is likely the word "brown"). It originated in County Limerick, but spread to SW Cork and is more common there now.
