No centralised RC registers in Offaly.
No census records for the 1800s. No vital records before 1864.
You need place of birth in County Offaly to find specific church which might have a possible baptism.
Without the specific birthplace, you can have Midlands Ancestry research it for you fee-based. Here's the link:http://www.irishmidlandsancestry.com/
Otherwise you need to research more in the US to find specific birthplace in Offaly.