Can you parent your black circle to the background layer? This way it would inherit whatever keyframe interpolation you have set to that layer. If your project is set up in a way in which this is not feasible, you could also create a null that does that movement and parent to that. If neither of those more simple solutions work, the are solutions involving expressions but I'd need more information about how your project is set up to best advise.
Just position your black circle the word supposed to be when it shows up in the scene and then make the moving background layer the parent.
Yeah, can you tell I haven't mastered Nulls and parenting. I was going to try this, but got distracted since the black circle has a life of it's own before getting to this part of the story. I'm going to try the simple parenting concept first. Create a duplicate circle that that come on the stage only where it follow the Parent background. Hide the earlier black circle too.
I'l post back. Thanks all!