Researching in Greece in that period usually means making use of dimologion -- a family group record kept by the mayor's office of each municipality. You will probably need to know the town or village your ancestors came from.
You can also check the mitroon arenon (male registers) for your male ancestors back to 1817 online at the Greek National Archives: [GRGSA-CSA] Central Service Archives (gak.gr)
There's also some provincial archival records online for Cephalonia, Corfu, etc. As most Greeks are/were Orthodox, there's also Orthodox church records available. Most records will be in Greek (obviously) and if you don't read/speak the language, I recommend hiring a local genealogist to do research and translations for you.
