Cooney, 27, will provide cover at scrum half after Luke McGarth picked up a knee injury playing for Leinster and was ruled out of the rest of the tournament.
Ringrose, 23, is drafted in to fill the gap left at centre by an injury to Robbie Henshaw while hooker Scannell, 25, fills in after Rob Herring injured his elbow playing for Ulster in the PRO14 at the weekend.
Ringrose has had to recover from an ankle injury of his own this year. He last played for Ireland against Japan in June, as did Scannell.
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Ireland have won their opening two matches in the Six Nations, and host a Welsh side who beat Scotland before losing narrowly to England in their second game.
(Reporting by Mark Gleeson; Editing by Kevin Liffey)
