A few approaches here, Julie:
Firstly, fire up the Clare County Library website search facility at
http://www.clarelibrary.ie/search.html and, using the Search For field rather than the Google engine, enter "walsh and kilkee and tithes" and take a look at the list of people who were "tithe applotted" in 1827. There's one John Walsh in Kilkee and other Walshes in nearby townlands in the parish of Kilfearagh.
Then do the same thing with "fitzpatrick and kilkee and tithes" and you'll find, among other relevant entries, a Catherine Fitzpatrick in Kilkee (the mother or grandmother of Mary ?).
Then search for "walsh and kilkee and griffiths" and "fitzpatrick and kilkee and Griffiths" for Walshes and Fitzpatricks listed in the 1855 Griffiths valuation. There are 4 Walshs and a Catherine Fitzpatrick in Kilkee in 1855.
The scent is strong, right ?
Then take a scale map of the area which shows all the townlands (an OS Discovery map is best), stick a compass in the town of Kilkee, draw a circle with a radius of five miles around the town, make a list of the townlands within the circle, and search the Library site for all mentions of Fitzpatricks and Walshs in those townlands. This is based on the genealogical rule of thumb that in rural communities in that part of the world 95% those without horse-and-carriage tended to marry within 5 miles of their homes because that was the distance they could comfortably walk to court in the evening and get back home in time for work in the morning (there were other reasons related to farm deals surrounding marriages but that's another subject).
Then fire up the Eircom residential phone directory at
http://www.eircom.ie and look for Walshes in Kilkee. The place is crawling with them. It is well possible that one of these present-day Walsh families is related to your ancestors and knows something about them. Emigrés sometimes wrote home and their letters were sometimes kept on mantlepieces and in kitchen drawers to the present day. Try phoning some of the Walshes in Kilkee and see whether they can help you. If you have the luck to get an elderly person on the phone you may be overwhelmed by the things you are told. If you get a young person on the phone and they haven't a clue about their family history ask them for the name and telephone number of the oldest Kilkee Walsh inhabitant they know. Then take it from there. Don't hesitate to cold-call in this manner. No-one will object if you have good phone skills and take a gentle approach. You may be staggered by the results. I speak from experience.
Best of luck. Let us know how it goes.
Paddy