The most natural way to do this is to use a negative sentence with a positive question tag at the end:
- You didn't give your note to him, did you?
You would say this with a high falling tone on did you if you want to show that you expect that the note was not given.
You could use a double negative in a question - but in that case you will want to stress the second not. Remember that if the auxiliary in the question is DO, then the main (i.e. lexical) verb needs to be in the infinitive:
- Didn't you not give your note to him?
Regarding the Original Poster's second example:
- Weren't you not giving your note to him?
This is perfectly grammatical. The meaning here is that the speaker thinks that your original plan was to not give the note to him.