For example, at the National Archives, Fermanagh lists the Parishes of Derryvullan and Aghalurcher (part only) for 1821. There appears to be fairly good survival for these localities. On the other hand, in Mayo the only surviving parish is Shruel (Shrule) and there was only one house (#6) in the townland of Ballycurrin. If you’re lucky enough, and your ancestor was in one of the places at that time, you may find a record for them. Using John Grenham’s website, in conjunction with his book, Tracing Your Irish Ancestors, will give you an excellent listing of what might be available. On his website, IrishAncestors, go to the sitemap, select the county, then the parish and in the upper right will be a list of sources. I struck out on census fragments…none in the areas of my ancestors.