In the 1970s, he attended Yale University, where he became friends and bandmates with harmonica player Jim Fitting, who would also become part of Treat Her Right.

[citation needed] When Mark Sandman formed Morphine, the original drummer was Jerome Deupree, but Conway served in the band for much of its existence.

The Rough Guide to Rock described him as playing jazz-influenced, very tight drums, but that he crucially left plenty of spaces for Sandman and the other member of the band, saxophonist Dana Colley, to make their noises.

Conway worked with Jeffrey Foucault and poet Lisa Olstein on the eponymous first album by Cold Satellite (2011) and the follow-up Cavalcade (2013).

Another part of this circle of artists is Caitlin Canty, whose 2015 album Reckless Skyline was produced by Foucault and employed Conway as drummer.

Foucault has cited a shared desire to give weight to space and silence, which was a constant in Conway's career.

[8] Conway was drummer on Early Riser, the ninth album by John Statz, recorded in 2019 and released in 2020.

Unfortunately, it was announced that week that Conway would not be able to perform at the event because of health issues and that Jerome Deupree and Larry Dersch would fill in.

This arose in his prior capacity as a founder of Hi-n-Dry, but he also oversaw two of Kris Delmhorst's albums, Five Stories and Songs for a Hurricane.