[1]: 67 Known as "The Bard of Dalymount", he was a co-founder of the band Sweeney's Men with Andy Irvine and 'Galway Joe' Dolan (who was later replaced by Terry Woods).

Sweeney's Men broke the mould of Irish music and are credited with starting the folk revival there in the late 1960s.

After Planxty, Moynihan replaced Irvine in De Dannan in 1976 and can be heard on their second album, Selected Jigs, Reels & Songs, released in 1977 but never re-issued on CD.

The other members were Swedish Lena Ullmann on clawhammer banjo and American Frank Hall on fiddle; in 2007, they renamed themselves Moonshine.

However, they reunited once more, this time billed as Sweeney's Men, for a one-off gig in Rostrevor, County Down on 22 July 2007, with Paul Brady deputising for Joe Dolan who was unwell.