It is possible for an object to be accelerating if it has a zero speed or zero velocity. In such a case, the object only has zero speed for an instant.
Two examples of objects accelerating with zero speed are a ball thrown into the air at its highest point and a pendulum at its highest point. In the case of the ball, it is under constant negative acceleration due to the force of gravity. Its vertical motion initially travels upwards, slows down, stops for an instant, then starts falling back towards the Earth. At the point where it stops for an instant, it has zero speed and negative acceleration. Similarly, in the case of the pendulum, the constant force of gravity slows its upward momentum, makes it stop for an instant, then causes it to fall back towards the Earth.