To have something so much and so often that the desire for it greatly decreases. Exhausted with something pleasurable because of the excessive presence of that pleasure. Especially with food.
To get sick of _____.
To have too much of a good thing.
To have a plethora of something delightful and but then the availability makes it loose it's zest.
I bet his booty calls with that girl are going to get cloy soon.
Having sex with a girl like that cloys after the 3rd or 4th time.
A diet of only cake cloys very fast.