I searched the Irish Family History Foundation's database. It has parts of Co. Roscommon's surviving parish rcds. Several parishes are not in it. ALL Irish rcds B4 1840 are sparse. At your estimated date of 1801, likely only 10-20% of all BMD events were being rcd'd.
For James O'Connor B abt 1801, I found 1 B rcd. This is for the yr 1804. This rcd MAY, or MAY NOT, be for your ancestor. The probability is at most 20%. There were lots of O'Connor's in Roscommon who were evicted and emigrated in the 1840s. If you view the detailed rcd, it MAY reveal info that will allow you to validate/invalidate it.
Google the Foundation's name to lead you to the database.