There are several bands with that name:
1.) Distant Cousins were an English band from Manchester. Some journalists grouped them with the "Madchester" scene, though their music rather was a blend of soul and pop. The band's singer was Doreen Edwards. Former member of The Smirks Neil Fitzpatrick played guitar, Simon Milner (vocals) and Ian Morris (bass) from The Smirks were also with them. "Snuff" (ex-Motivation) played drums and percussion.They were originally signed to independent label Ghetto Records for whom they recorded their first album Distant Cousins. A re-recording of one the album tracks You Used to became their first single. Recorded in Studio 2 at Abbey Road it was produced by Mike Hedges who also produced their second album Warm Hatred at his own studio in Normandy. The band were then signed to Virgin along with label stablemates The Lightning Seeds. The band were at one time barred from a Dutch hotel chain due the antics of their road crew, who they shared with The Stone Roses.
2.) A New York based roots rock band with female singer and guitarist Cat Dail who recorded the albums Love Life in 2001 and Twice Removed in 2007 that are featured with streamable tracks on this page.
3.) A Bluegrass band from Alabama with Kelli Johnson (voc).
4.) A Bluegrass band from California with Bridget Brennan (voc). .