The clunking specifically occurs at downshift. It occurs in each downshift.

There is also a clunking when I put the car in park and it has a gradual shake from side to side or a rocking. When this is going on I hear a clunk, clunk, clunk, coming from the rear of the car until I turn the engine off. It does not do this at a stoplight with the car in drive - only when car is running and in park.