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Some possible leads
I checked the 1855 Griffiths Valuation head of household listings for Co. Clare and there were three John Davis records. Two of the three were from southern Co. Clare. One of the records was in Ballinaboy civil parish which is south of Ballyvaughan. The corresponding RC parish is Corrofin which corresponds to the 1868 marriage. John Davis and his family lived in Corrofin town in the townland Baunkyle.See link http://www.failteromhat.com/griffiths/clare/killinaboy.htm
I searched for an Ann Davis baptismal record and there was an 1836 record in the Rath/Ballinaboy/Corrofin parish but the mother was a Bridget Casey. (Ignore the surname of the father as Casey. The program that read the record made a mistake). Here is the parish register for Rath/Corrofin http://registers.nli.ie/parishes/0799
First name(s)AnnaLast nameDavisBirth year-Baptism year1836Baptism date27 Jun 1836ParishRathAlternative parish namesCorofin, Kilnaboy, Kilnaboy and Rath, Rath and KilnaboyDioceseKillaloeCountyClareCountryIrelandFather's first name(s)JoannisFather's last nameCaseyMother's first name(s)BrigidaMother's last nameCaseyRepositoryNational Library of IrelandNational Library of Ireland linkhttp://registers.nli.ie//registers/vtls000634752#page/1/mode/1upRegisterBaptism