James' birth is included in the extracted civil birth collection on FamilySearch, and confirms the parents names you mentioned :
Name: James Redfern
Birth Date: 30 Apr 1874
Birthplace: Lusk, Dublin
Parents : James Redfern & Eliza Connor
Ref. : v 7-1 p 461
Lusk is a sub division (also a town) within the Balrothery district, and includes the town of Rush. The birth cert mentioned above would give a bit more detail, such as father's occupation etc
Shane