I'd definitely give UA a look. Aer Lingus (EI) is also a UA partner and their availability will show up on the UA website for award searches. Not to mention other UA partners who may be available. And if you wanted you can set up an open jaw or a stopover with a UA roundtrip redemption, at no additional miles.

A quick look at random July dates seems to show pretty decent availability PHX-DUB. UA doesn't pass along any fuel surcharges on redemptions through its FFP.