(Sorry; I can post only in English)
I didn't see too many references to the Irish band Republic of Loose on here, so here's a list of their collaborations with Sinéad.
"We People (Who Are Darker Than Blue)" - not the same version on Theology. Released digitally in February 2009. The only physical copy of this song is on a promo CD along with "Back Where You Belong".
"The Telephone (feat. Sinéad O'Connor)" - Sinéad does backing vocals on the chorus of this rather awful song from RoL's 2008 album Vol. IV: Johnny Pyro and the Dance of Evil (released only in Ireland, and hard to find)
"You Can't Do That" (cover of the 1964 Beatles song) - performed live at a benefit concert in Ireland last February, and released for one day only (June 13th, 2009) on a CD distributed free with copies of the Irish Daily Mail. I've ordered a copy on eBay; it's in the mail right now.