I would not know where to search for British merchant Navy records but that is the
first place I would look for further info. Without further info trawling through Irish records could be very formidable.
There was a John Donovan who ran a posting establishment in Rosscarbery in The Square. A posting establishment may also have been an inn or affiliated with an inn. It was sort of a place to park the horse while in town to do business. This is in Francis Guy's County Cork directory from 1875 (see Cork resources).
These are the only baptismals I could spot in the church records in the Rosscarbery RC parish of John Donovans whose fathers are John Donovans, the few years leading up to 1872:
27-Jun-1866
http://churchrecords.irishgenealogy.ie/churchrecords/details/5d178f026416515-Mar-1869
http://churchrecords.irishgenealogy.ie/churchrecords/details/925ce5026457226-Dec-1869
http://churchrecords.irishgenealogy.ie/churchrecords/details/9c8cd10264699You can easily extend such a search to look at more RC parishes.
If you want to pursue these, you can look up these approximate dates in Family Search Irish Civil Registration and either order the certs from GRO or look at the films in a local family history library.
If you look for these in civil registration, anybody born late in the year might have been registered the following year.
You can also search the Irish special collections, Births and Baptisms. Enter John Donovan for the Name, set Relationship=Parents and enter John Donovan for the father, then restrict the date range as much as you want.
This is not a "complete" collection so it won't be an exhaustive list.
If you order any certs or look at any films of possible leads, the registry entries will state the father's occupation.
https://www.familysearch.org/s/collection/show#uri=http://search-api:8080/searchapi/search/collection/1584963For what it's worth I have found that when I am on a fishing expedition for the money it is by far the best to rent the film at a local library and look exhaustively at ALL places of interest.
I looked at the census, but without further info, it may not be very helpful. If you happened to know if the father was still alive, you could search for John Donovans in Cork, sort by age, and just look at the oldest ones. You might also want to experiment searching on occupational words such as "hotel", "inn", "proprietor", "vintner", "bar owner", and "publican." I also looked for women named Donovan who were from France, but turned up nothing.
http://census.nationalarchives.ie/search/