At FTDNA.com I have recently got a Y Chromosome match with a Kaney having previously having had matches with Kenneys.
This got me thinking and leads me to conclude that both Kaney and Kenney are indeed sometimes derived from the old Irish surname of O'Geibheannaigh (Keaveney). In Ireland, the O Geibheannaigh surname is often pronounced as Geaney or Guiney; Kaney or Kenney is just a version where G is replaced with K as also in the case of Keaveney.
Not all Kaneys surname histories will fit this scenario but some definitely will. Other related surnames are Kaveny, Cavney and Kevan and a small minority of CavanaughKavanaughs.
The related surnames would come originally from counties Galway and Roscommon in the West of Ireland. The Keaveney surname dates from 972AD approximately as mentioned in the Irish Annal: The Tribes and Customs of Hymany.