This is my first foray into Irish records, so am not sure what I am doing

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Bernard Riley birth about 1791 Died 1868 Ardsley W.Yorkshire.
Mary Bowen birth abt 1799 died Ardsley 1869.
Their first child was born in 1826 in West Yorkshire, so assume they were married prior to this.
From various sources we have for Bernard, Courtmatrix, Limerick or Galway.
for Mary possibly Galway.
This is all the info I have and really do not know where to start

I suppose a marriage would be a start, but when and where

All help appreciated, as I am in Australia records are a bit difficuly.
Thanks in anticipation...Patvp