Difference between two structures

a) I rely on you to come in time.
b) I rely on your coming in time.

  What is the difference between the structures above all things considered 
  (e.g. formality,variety of English, and so on)

     Many thanks...

Both are possible. The first places more emphasis on the action according to some.

Above all, thank you for all your replies.
My teacher said that only (a) is natural. How would you react to my teacher’s opinion?..

I would guess that your teacher is not a native English speaker and is relying on traditional rules.