"nothing doing" is more of a refusal to do something. It may or may not be possible to do it. "nothing can be done" is more of an excuse or reason for not doing something. You are saying it is not possible to do something.

right and wrong. :P

"Nothing doing" is incorrect. You can say ". . . . "doing nothing" as in "I am doing nothing for Christmas". As previously implied "nothing can be done" is a correct statement.