Strange Noise, Driveshaft?

I don't know why it seems I get all the strange problems, I have asked 8 mechanics whom I rely on for expertise and knowledge and they are all scratching their head on this one.

I will start from a dead stop, bring it up to 10 mph, let off the gas, then slow back down. I can either hit the brakes or not, doesn't seem to matter. But what it seems like to me, and I could be wrong, is that when the engine stops pushing the car and the car starts pushing the engine, I either hear a pop, ding, or boing noise, and sometimes, like 2 out of 6 times it won't make any noise. What the hell is that?

If you have any questions, ask away. This one is really got me wondering. I have never heard a noise like this.

Thanks