McCoy. Although I don't really agree with how they arrived at that the origin of his nickname. Although his introduction (that of his ex-wife having left him with nothing but his Bones) can be seen as somekind of cinema shorthand to clue an audience in quickly of who he is. In my mind (Yes, I know... fanon isn't canon), McCoy was called "Bones" because of "Sawbones", an old term for a Doctor serving in the military in historical times.
I humbly disagree.
I think the origin that Orci & Kurtzman came up with was brilliant (and those that know me know that I don't use Orci, Kurtzman and brilliant in the same sentence very often). The reason being that no one on the ship called McCoy "Bones" except Kirk. That to me suggests the nickname could be something private between the two men.
As in all things, your mileage may vary.