When Roady (or usually Rody) is a suffix it usually is associated with the Ryan family - the Ryan Rody's. In my Ryan Rody line I was told by my grandfather (born 1890s) that it is derived from their red hair ( ruadh in Irish.) If it is for e.g. Roddy Ryan, it is most likely that it is from Rory, (ruaidhri in Irish) which name is anglicized as Roger.
K.