I wouldn't bother stirring it. It will mix fairly well as is. You could even add it to your bottling bucket, as the coffee isn't really going to change any during the fermentation process. If you do add it to the primary, when you rack it to the bottling bucket, it will finish any mixing that it didn't get in the primary.
In fact, I would say it would be best to put it in the bottling bucket, though, since the yeast won't absorb any of the coffee flavor.
Secondary: Bee Cave Robust Porter (with coconut)
Kegged: Cascade/Citra Amber Ale