An old thread, but emmaodea111 and others, I am also researching Cunninghams from Clare, but living Turnpike in Ennis at least 1842 to after 1872. Not sure where from originally, though John O'Hart traces his grand-daughter Bessie Cunningham/son-in-law John Cunningham's line back to Rodger/Roady O'Cunnivane born 1680, four generations back from Thomas Cunningham who died 29 November 1869 at Turnpike aged 88 (informant: Mary Cunningham) - transcription from Rootsireland (Deaths Register for Ennis, Co. Clare, 1870, Vol. 4, page 179). From Roady we have Timothy, Darby, Mihil/Michael, Thomas (aforementioned) and then Michael Cunningham (married Mary O'Brien in 1842; likely the Mary Cunningham above).
The four previous names and indeed earlier Anglicisation of O'Cunnivane may be reliable enough given John O'Hart's direct relationship in this case (certainly I imagine he tried to go back further than Rodger). Maybe looking for O'Cunnivanes or variations will help with other Cunninghams in Clare?
I really don't have much to go on besides the descendents around Turnpike and possibly a couple of other Cunninghams as witnesses at births/marriages! Seems likely they didn't have roots all the way back specifically in the Turnpike area of Ennis. I've loads more info if anyone needs it on the events of that particular family from mid-19th C on though.