Ythanside - I don't think the name coney derived from coineen, rather they both derived from the same Latin source. For con(e)y OED gives earliest forms cunin, cuning adopted from Anglo-French coning, Old French conin derived from Latin cuniculus. As the Celtic group descended from Latin I presume they had the same Latin source.

Of puss, Partridge's Historical Slang gives the sense of hare as colloquial 19-20th centuries.

Mick