If the displacement covered by the body is zero then the average velocity is zero. 
But the distance covered by the body can't be zero,so the average speed can't be zero .
First we need to understand what is average velocity and average speed.
Average velocity=Total diplacement/Total time
Average speed= Total Distance/Total time

If a body travels from Point A to Point B and then again travels From Point B back to Point A, then-
Displacement = 0
Distance = 2AB

(Point-A)                                     (Point-B)

Therefore, since displacement is zero, then avg, velocity will also be zero but avg. speed would not.

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but I think one of the body with 0 velocity but non zero speed could be the planets, revolving in their fixed elliptical path.