I searched the Irish Family History Foundation's database. It contains abt 60% of the surviving rcds for all Ireland. Rcds B4 1840 are sparse.
For the name Patrick Haley (+variants) B 1829 (exact) in "all Ireland," I found 0 matches. Assuming Margaret and John married abt 1820, Patrick is likely the middle child. This infers that you are unlikely to find B rcds for his siblings either.
My guess is John Haley most likely died of famine related illnesses in the 1840s.
Suggest you google the Foundation's name and browse the database.