I checked MacLysaght's Surnames of Ireland (a very fine resource) and he offered this: Cooney/Ó Cuana is probably of the same derivation as Coonan/Ó Cuanáin. Further, Cuanán is probably 'cuan' meaning 'elegant' with the '-án' diminutive suffix.
Two 'probablies' in two separate entries is not encouraging, but this guy knew his stuff and I believe the lack of the accent/fada on the first 'a' (Cuana vs. Cuána) gives credence to the theory.
This contradicts Anneza's thought connecting it to Cuán meaning 'little hound,' but that would certainly be my second choice. The only subject on which I disagree with her is the presumption of '-a' suffixes on Early Irish names. This was neither common for masculine nor feminine names.