Looked high and low for your Daniel, but found nothing in Irish records.
I had a few credits left on Scotlands people (
http://www.scotlandspeople.gov.uk ) , and had a look for a birth between 1855 and 1865. I know it appears from Census records that he was born in Belfast, but this may not be the case, especially as no birth record can be found.
There were 5, dating between those years, notably two in Dalry in Ayrshire.
I had a look at those two, and one was born to a Daniel Barr and Elizabeth Kilpatrick on 8th June 1858 at 00:30. Daniel the father was an Iron Miner.
Unfortunately I dont have any more credits left to use for you, but i think this record is a real possibility.
I'll send you the details by P M , in case I infringe copyright.
If he was born in Belfast,and you have a resonably accurate year of birth, then the GRO in Belfast should be able to find his birth record for a small fee (
www.groni.gov.uk/ ) but if he was born before 1864, then Church records are your best bet.
Good luck
OTTO