You don't mention religious denomination but I will assume Church of Ireland. The records for the Carrigallen Church of Ireland parish were lost in the 1922 Public Records Office fire and are not available. If I'm wrong about the religious denomination, please let me know. I was not able to locate a marriage record for William Wood and Mary McKinlay.
The 1857 Griffiths Valuation head of household listing for Carrigallen civil parish showed four William Woods records in four different townlands. Not sure if there were four distinct William Woods or if one or two William's had two properties. Possibly one was the father of the 1837 William.
Let me know if you have any questions.