Step down transformer without coil?
Is it possible to make a step-down CIRCUIT without coils? 

Sure, we typically call them "lamp dimmers" or "motor speed controls", etc. etc. There are millions of examples all over the globe. There may be one within a few meters of where you are right now.

Is it possible to make a (whatever) TRANSFORMER without coils?

No. By definition a transformer (in the ordinary sense) is made with one or more windings ("coils" if you will).