I searched the Irish Family History Foundation's database. Portions of Roscommon's rcds are in it. Contact email@example.com for those parishes which aren't.
For Patrick Dunican (+variants) B 1840 +/- 4 yrs, I found 2 B rcds: 1 in 1837, the other in 1843. One of these MAY be your ancestor. However, so many of the rcds remain undigitized, there is only abt a 25% chance of this being true.