I'm afraid I'm just going to muddy the waters.
MacLysaght's "Surnames of
Ireland" (which I trust rather implicitly) derives
Delaney as an Anglicized form of Ó Dubhshláinne. The rootwords are 'dubh' meaning 'black' and possibly 'Sláine' as in the river Slaney. This particular surname originates in Counties Leix and Kilkenny.