Hi:
I read your Ancestor Profile and there may be some avenues to research using the Clare records. Did John McInerney have any siblings that emigrated either with him or after? I would be very surprised if another family member or cousin (or neighbour) did not also come to the Manchester area.
The two surnames of McInerney and Jones are very good clues. McInerney is a very common Clare surname, but Jones is limited to less parishes and I would recommend that you concentrate on those parishes where both surnames exist. Pre-Famine, most marriages took place between marriage parties who lived within 5 miles of one another. The parishes where the Jones surname exist are predominantly in East Clare: Tulla, Clooney/Quin, Moynoe(Scariff), Tuamgraney, Killaloe, Killuran, Feakle and Kilfintinan. The other areas are: Dysert, Rath, Inagh and Clondegad. The McInerney name is more numerous and widely scattered, but if you look at the Clare Library website under the link here: http://www.clarelibrary.ie/eolas/coclare/genealogy/tithe_applot/name_index/index26_IeversToJurdon.htm , you will see what I have written above. If you look at the McInerney surname list location, I would check which parishes are also Jones surname parishes. I would then concentrate my search on those places with both surnames.
If you have any questions, please let me know.
All the best,
Jane