I've used coconut a number of times in a milk stout recipe of mine. I've added the coconut both at the secondary conditioning stage (using a fermenting bucket), and a couple of occasions I've added it into the keg when short on time. When adding the coconut into the keg, I'll use a partial mash grain bag to contain the coconut (approximately 2 lbs of flaked toasted coconut usually). It is a PITA to get the bag of coconut out of the keg once the coconut has become saturated with beer. And the keg opening is pretty substantial. I imagine that if you ever did manage to fill a bag with coconut flakes in a carboy, there would be no getting it out.
Definitely just get a fermenting bucket or big mouth, and condition in that.