Dear Mary,
Don't lose heart! I've found quite a lot of information. I am fortunate that many of my folks were long-lived, which meant there were more records. Anyway, this is as far as I've got:
Carefully reading census images gave the townland and county of three of my relatives (Newport and Longford in Mayo, and Belfast). Once people filled the census forms in themselves, rather than telling a stranger, they added more information, I found.
This information is not always transcribed, in fact it was often crossed out by enumerators, so looking at the microfilms of the originals is more useful than simply going by the typed transcripts.
I found the baptisms of my Roscommon ancestors on Familysearch a few years ago. I picked the person with the most unusual name (so not Bridget or Patrick) and searched as many variations as I could think of until one turned up. Then I found all the other siblings. Their ages all fitted with the English censuses. I searched for Rose Patterson. Eventually I found Rozam Patterson and that was her. This took a lot of trials of different surname and first name/ initial combinations. Be patient! This then told me that they were from Ardcarn in Roscommon.
I'd advise you to have a look at some lists of Latin versions of Irish/English names. I searched forever for an ancestor called Owen before realising he was down as Eugenius. Please note that Patrick is often written as Patt, and Bridget as Biddy or Bidy.
I found the county of origin of one of my ancestors by getting a transcript from the old people's home he lived in; he was born in Co Galway in the 1830's . The home was run by the Little Sisters of the poor and closed in Sunderland only in the last few years. I found him on the census there in 1911. I asked them for his records and they also came up with the names of both his parents. So if they lived in an institution run by a catholic religious order I'd suggest you follow it up.
I think another part of my family are from Monaghan. I noticed that the same informant cropped up on a lot of death certificates and it said on one he was a brother in law. Anyway, I looked at the censuses for this person, who was from Monaghan. I have not yet followed up this lead.
If you manage to find a county, you can try the local records. A lovely American correspondent of mine, whom I found through Ancestry, tells me that the various Family History Centres (each county has one) are very helpful. I haven't tried them yet. She deals with them by email.
You could also search the Irish Tithe Applotments and the Griffith Valuation databases. I've tried to include links and my iPad won't let me, but Google them and have a look.
The National Library of Ireland has just published a load of Catholic parish records between about 1830 and 1880. You can't search them but have to trawl through the register pages. These are interesting - often the priest annotates the records with subsequent deaths of marriages. I found my 4x great grandfather there yesterday (yay!).
Sometimes, your relatives' names can lead you to a particular region. For example, from my family, the name Wafer is pretty unusual and mostly confined to wexford. Coyne is much more common in the West of Ireland, especially Galway. I gather that the name Lavelle is confined nearly entirely to Mayo. Names that sound more Scottish (in my case McAllister) tend to be nearer to the North of Ireland. I have also noticed that some first names are more common in some areas - this is not at all scientific- there are a lot more Honors and Winifreds in the West of Ireland than in Wexford and a lot more Anastatias in Wexford than in Mayo. There seem to me to be more people with Irish names (eg Tadgh, Sabby, etc) in the West than the East. There is a website called youririshheritage.com that shares information on surnames. It's very chatty and not really my style, but they email tens of thousands of people their newsletter every week, so they must be doing something right. There are other more factual websites too.
You could try putting names into the Irish 1901 and 1911 census (free online) - you may find a load of people with the same names all living in one area, which could be a lead.
There is a pay website rootsireland.ie that has some records. It used to cost FIVE EURO PER VIEW (yes, really). I think the membership payment structure is different now. I don't use it because when I last looked they didn't have wexford records, which is what I needed t the time. I did find one baptism (Belfast) on there that was very useful, but I can't really comment on it. Perhaps other members can.
This has all taken FOREVER, but it was worth it for me. Now O have the counties and some parishes I can move forward, I hope.
I have also decided that, since I may not be able to go back much further, I will read up on the local history of the counties from which my relatives came to try to get close to them that way.
I hope it works out for you.
Cx