Thanks Jambo - I was familiar with CG66 and we don't have an informal arrangement like that here. I also had missed that Barrowboy and his boat are now based in Galway so I'm no longer looking at the question in the same light (i.e. he's not visiting for a holiday etc.)
OP - the system here is straightforward. If your RIB was local previously then there is a good chance (but not a certainty) that she has a radio licence and associated callsign (begins IE####) and MMSI. That is generally the most "registering" small Irish craft get. It does however place her and her owner on a database that the CG use for safety purposes. Details of the system are here:
Maritime Radio Affairs Unit (MRAU) | DTTAS Department of Transport, Tourism And Sport
The lifetime licence cost is Euro100 but you can transfer ownership and update details if previously licenced/registered.
If you have taken a UK registered vessel to operate here for a short period then I would suggest using the local CG radio station to place daily TRs. Irish CG are generally happy to keep track of small craft as they are relatively quiet.