I'm doing an editing project for some folks which involves overlaying their video with pictures. They are complaining because there is a sudden transition from the video to the picture and vice versa. I can employ a fade in and fade out effect, but they don't want the screen going black. Is there any other effect or technique I can employ to make the transition less noticeable?

Use a Composition effect and select Dissolve. The clips need to overlap for the duration of the transition.

Arrange the clips in the timeline on V1 and V2 with an overlap, then click the grey circle (hover the mouse where the clips overlap). That inserts a Wipe composition with the standard Wipe Method None (Dissolve). ALternatively, put the clips next to each other in the timeline with one of the clips slightly trimmed on the end or the start, then select one and click the checkered box above the timeline. That does the same but it's called an inline transition