Air Conditioning - Rattling noise coming from handler

Our A/C works and is cooling, but suddenly one night several months ago, it started making a squealing noise followed by a rattling sound. We had a repair man come out and he replaced something in the handler and the squeling has gone away, but it still rattles at the end of a cycle. The squealing is definitely coming from the handler because it is only heard through the vents in 2 bedrooms closest to the handler.

The system comes on and works fine. Both the outside fan and handler working normally. When the outside unit cuts off, the inside handler continues to blow cool air, that's when the rattling noise starts. After several minutes, the handler cuts off. When the unit kicks back on, it works normally until the outside unit cuts off, then the rattling starts again. Like I said, it happens at the end of the cycle.

Repair man comes out and checks the basic stuff, and says that he can't find anything. This noise makes it hard to fall asleep because the handler is downstairs directly under my bedroom. Can anyone suggest a fix?