Locating a family in Ireland before 1750 without many specifics to go on is close to impossible. There is no comprehensive nationwide census, index, or database in that time period that you could search without knowing a fairly specific locality with certainty. Even if such a finding aid did exist, you would have to have enough identifying information on your ancestral family (or an especially unusual name) to have any confidence that the person you found was not someone else with the same name as your ancestor.
About the only way I know of to place an ancestor in Ireland before the early to mid-1800s is to exhaust the resources in America, Canada, Australia, or wherever your ancestor migrated to, not only for your known ancestor but any possible relatives and associates. Perhaps more than any other ethnic group, the Irish migrated in groups and settled near relatives or people from the same community in Ireland. If just one of your ancestors' relatives or associates left a record pointing to a specific Irish location, you could have an excellent starting point.
Even with such a broad-based search, however, you will need exceptional luck to tie a 1750s immigrant to a specific location and family in Ireland (unless of course your ancestor was one of the relatively few wealthy or land-owning families). Once you do locate the ancestor in Ireland, there aren't many records available that early. Some church records -- mostly Protestant -- do exist back to the early 1700s (and a few earlier), which are extremely helpful.
Probably your next best resource is the landed estate papers of whoever the ancestor's landlord was. If they can be found, these papers can contain many useful clues to help you piece together a family and perhaps add some generations. (For an example of how this can be done, see my article, "Organizing Meager Evidence to Reveal LIneages: An Irish Example -- Geddes of Tyrone," , National Genealogical Society Quarterly 89 (June 2001): 98-112.) Irish landed estate records can be found in several repositories across Ireland and England (many of the landlords lived in England), but many others are inacessible or lost.