One of the main reasons most (if not all) trainers are tricycle gear (nose wheel) type of aircraft is that they are easier to steer on the ground. Once the tail leaves the ground during take off roll on a tail dragger, ALL steering is rudder controlled and can vane into the wind if left unattended. This is why we are taught to hold a little up elevator during initial roll on take off, or at least I was taught that way. This is to aid in tail wheel effectiveness for the first few yards of roll-out on take off. Once this is released, the tail wheel immediately lifts up off the ground and the steering is totally rudder controlled.

Steering a trike is easier because once the nose wheel leaves the ground (and most... MOST) of the steering which was controlled by this wheel loses effectiveness, well, the plane is airborne and flying.

Now to answer your question, I don't know of any real trainers that are tail draggers. There may be some, but I am not aware of any. Perhaps some others have a better answer to that than I do.

CGr.