In 2004 vocalist, songwriter, actor, horn and guitar player Sean Lynch (formerly of Cygnet Committee, Hand of Glory and Alla Zingaro) and percussionist/multi-instrumentalist Peter Caldwell (whose credits also include both Hand of Glory and Alla Zingaro, as well as Tsunami Band and Big Muffin Serious Band) formed Conway.
Stan describes the project as "low-key dark folk". They have been playing some low-key gigs between Auckland and Hamilton.
Conway's performances are infrequent, in February 2015 the band hosted an evening and headlining set at The Meteor, supported by Phantasy Gang and Ancient Tapes. The band played an hour set, with the line up extended to include Nick Johnson (Sora Shima) on keyboards, with Gareth Schott (sink \ sink, Ancient Tapes) joining them on guitar for part of the set. The same extended line up appeared at the Meteor in June 2016 in support of its Earthquake fundraiser and Zeitgeist: Bowie evening (links below)
The band contributed the song Broken to the 2020 compilation In Thrust We Trust.