I apologize as I misunderstood your request.
However, a second search produced only a couple of records that could belong to your Robert.
Ireland, Landed Estate Court Files, 1850-1885
Name: Robert Carson
Event Type: Probate
Event Date: 1855
Event Place: Galway, Ireland
Document Number: 051
Volume Number: 033
Volume Date Range: Jan-Feb 1855
Alternate Event Pace: Fough West
Ireland, Prison Registers, 1790-1924
Name: Robt Carson
Role of Individual: Victim
Event Type: Prison
Event Date: 1852
Event Place: Galway, Galway, Ireland
Offense: Tearing & Scattering The Leaves Of A Certain Book Called The New Testament In The Streets Of Outerard On Oath
Item Number: 3
Book Number: 1/21/4
GS Film number:(NNN) NNN-NNNN/p>
Digital Folder Number:NNN-NN-NNNN/p>
Image Number: 00775
The only other Robert Carson I have located has the middle name of Haldane.
I have access to all available records online, which is where all of our research is done. Many Irish records have been destroyed and what is left is not entirely online. In fact most of the records used in Irish research are not vital records or church records, and these records are not "popular" enough to be placed online as the return on the investment is minute.
I wish you good luck with your search.