Chief762x39

I have a weird problem I'm trying to diagnose. Ever since I purchase my 1999 Firebird Trans Am (about 6 years ago) I have occasionaly heard a clinking sound (usually a quick "clink clink") when the car is shifted into reverse or shifted from reverse into drive. I occasionaly hear it when I move forward after stoping at a stop sign too. The car has an automatic transmision. I took it too a local mechanic who replaced the Ujoints but that did nothing to fix the problem. He checked the transmission mounts and says they are good too. Using one of those automotive stethescope things he listened under the car while someone else shifted from drive to reverse and determined the noise is probably coming from the transmission, rear end, or the drive shaft. Replacing any of the parts is not cheap and he wasn't able to tell me for sure what it was. Any ideas? I'm asking here to see if perhaps this is a common problem others have encountered. The car seems to operate normally.