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I searched the subscription site Roots Ireland and only located one baptismal record (see below) that was around 1835 and had the correct parents names. Lisdowney RC parish is to the west of Muckalee RC parish which would be the parish for someone living in Kilmadum civil parish. Not sure if this record is for your John Delaney. I also searched for Mary Walsh baptismal records around 1840 with the parents names you provided and there were too many possibilities. It would really help if you could locate the maiden name of either mother. I did not find a marriage record for John Delaney and Mary Walsh.
I did check the 1849 Griffiths Valuation head of household listing for Kilmadum civil parish and there were seven Delaney records inclusing a Daniel and a William. The Daniel may not be the same person who had a mine in New York State.
Let me know if you have any questions or have additional information.
Name:John DelanyDate of Birth Date of Baptism:19-May-1830Address:SpawhillParish/District:LISDOWNEYGender:MaleCountyCo. Kilkenny
Father:William DelanyMother:Honor LyonsOccupation:
Sponsor 1 /
Informant 1:Martin PhelanSponsor 2 /
Informant 2:Catherine Lyons