Muirgheas Ua Cú Ceannainn (died 1106) was King of Uí Díarmata.
The Annals of Ulster record that "Niall Odar ua Conchobuir was killed. Muirgius ua Conchenaind died.", but no connection is drawn between the two events. Muirgius's apparent successor was Aedh Ua Con Ceannainn.