The Care Bears Movie
The first time the Cousin Call was attempted towards the end of The Care Bears Movie, the Cousins all made their respective animal sounds in an attempt to aid the Care Bears, but because they did not have belly badges, it had no little effect.
The Cousin Call became most effective when the Cousins recieved their Belly Badges.
Care Bears Movie II: A New Generation
The effects are nearly identical to those of the Care Bear Stare, and most likely shares the same general process (focusing the user's emotions and caring into their symbol, thus projecting it outward)