What is the direction of acceleration of an elevator that is moving upward and speeding up?

The sign is difficult to determine because you have not assigned a sign to direction.

A) Moving down and moving at increasing speed means that it is accelerating down. So it is accelerating in the same direction as motion.
B) Moving down and slowing down, means it is accelerating up (which sounds strange, but I am trying to follow your convention). The direction of acceleration is opposite of the direction of motion in this case.
C) Acceleration's direction has nothing to do with the direction of the object's movement. Acceleration is in the direction of the change in motion.