1) are you sure he is from Kerry because if not then he could be from a different county that does have birth records on line. There is an Irish Heritage Foundation that has parish records from all but 3 Counties and Dublin City. Those would still have local genealogy offices that you can find by googling.
2) age, do you have a close birth year, which would help me
look for what's available. For instance www.familysearch.org
has Civil Registrations from 1864-1950's, plus US Census in some cases. Prior to 1864 all records are parish records many of which were destroyed by fire in 1922.
different information from each Parish.
Also rootsweb has some county information you can access from the main page.
I looked at the Griffith Valuation 1853 for Kerry looking for others name Jeremiah that could be father or grandfather. Jeremiah is quite rare in most counties however,in Kerry there are 292 Jeremiah Sullivan's. I expected lots of Sullivan's but that many Jeremiah's !!!
I checked the commercial directories for the name as there
are several from 1846-1894 but if he was a farmer he wouldn't be listed till about 1881.
These would then be just examples as you don't have where in Kerry.
1870 Castle Island Jeremiah Sullivan, Main St. Grocer
1881 Tralee Jeremiah Sullivan Castle St. Public House
1881 Tralee Florence (keep in the family?) 80 Boherbee,Shop Keeper
I checked a couple of US Census to find that there is either another Cheston T. Sullivan or is the same person but one had his father born in Ireland and the other his parents were not born in Ireland and the ages are born 1882-1966 or March 1879. Both Pennsylvania.
There are two draft to armed forces WWI & WWII.
My CD collection is not cooperating at the moment or I would be able to look up the civil registrations from 1864-1875, it is better than the website for www.familysearch.org
it comes with parents names.