If you have a look at Church Records (Baptisms) in irishgenealogy.ie from 1835 to 1839 in the Diocese of Cork & Ross you will find at least four Cornelius Donovan's with a father Denis Donovan. I am not saying that any one of them are your Cornelius as you dont know thw name of his mother but there might be some tiny little detail in there (like their address or their sponsors name) that stirs a memory that can help direct you.
These are not the only Cornelius Donovan's in Cork County where the name Donovan occurs so frequently that even knowing the mothers maiden name is not a guarrantee that you have the right family as there are many Donovan spouses that have the same name too.
Sorry for being so negative but the records for that era are incomplete and can also br quite inaccurate. In the 1901 Census, there were 221 Denis Donovan's who certainly are not your Denis but just to give you an idea of what you are dealing with. By the way, I am not mis-spelling Denis, in Ireland then and today it is the usual spelliung and not Dennis
Also sorry that i dont think I can help you more in your search because as you said " Not much to go on really" but will be happy to try if you think of anything else to tell me.
Frank