"Why not Tuesday?"
Translation:Perché non martedì?
Where have you seen it without an accent? It should always have one. http://www.collinsdictionary.com/dictionary/italian-english/perch%C3%A9
We don't have enough information here. The previous conversation could have been : "What day of the week do you like? I like every day except Tuesday. Why not Tuesday?" Here it would not be appropriate to add "on" We just don't know if this is a conversation about doing something on a day, so without context we just can't add that word in.