Icelandair has round-trip flights from Portland (PDX) to Dublin (DUB) for $587 with a connection. Flights September to October. Departures on Tuesday, Wednesday, and Sunday.
Note: Some small OTAs on Skyscanner have this for $550; cheaper than the airline. If you plan on booking there, beware of any site that charges a fee to cancel a ticket within the 24-hour “free” period. Use unknown booking sites at your own risk.