I did find a couple (only) of Reilly items in the web-accessible holdings of UCD (University College Dublin). You can see them as items 3 and 4 that come up in the following search:

https://digital.ucd.ie/?q=%22John+Reilly%22&rows=48&start=1

They are "False Lankum, sung by John Reilly, a Traveller, who was camped at Cloongrehan, Cootehall, County Roscommon" (TM0015 Side A)
and
"Reel - The Sallygardens, lilted by John Reilly, a Traveller, who was camped at Cloongrehan, Cootehall, County Roscommon" (TM0015 Side B).

I would imagine that there should be a lot more of the Munnelly recordings of John Reilly there, but maybe they are not digitised as yet.

Regards - Tony