O'Laughlin's "Families of County Galway" says this about Feeney:
O'FEENEY, Feeney, Feeny, Finny, Finney
Feeney families will find that their name is traditionally associated with the province of Connaught, particularly in the counties of Sligo, Mayo, Galway and Roscommon.
There were two familes in Connaught which assumed the name of (O) Feeney. One was O'Fiannaidhe of Mayo and Sligo and the other was O'Fidhne of Galway and Roscommon counties.
Feeney was the most popular spelling of the name in the 1890 index, with some 46 births recorded in Sligo, Mayo and Galway. 'Feeny' had 26 births in the counties of Galway and Roscommon. (see "The Book of Irish Familes, great & small" for additional entry)