kingskerswell , my Sister has traced the death certs for both Matthew and Mary Elizabeth. They give parents as ( Mary Elizabeth ) indeed as you say , but for Matthew , they are Robert Cairns and Elizabeth Ann McEachran.
McEachran is possibly another spelling of McCaughern which is a common surname in the Rasharkin area- with many spellings.
IGI lists 2 children for Robert Cairns and Eliza Ann McCaughern:
1. Rosetta Cairns born 28 July 1870 Co. Antrim
2. David born 21 June 1877 Carrefenton, Co.Antrim
Note: there is a Carnfinton townland in Rasharkin Parish.
Emerald Ancestors index has possible match:
Robert Cairns m.1859 Co.Antrim Eliza Anne ?
Eliza Anne McCaughern m.1859 Co.Antrim Robert ?