drop-me-nots can be found in chests throughout the worlds (a total of 18 for sora and 19 for riku), as well as enemy drops from peepsta hoo, tama sheep, majik lapin and me me bunny, all with a drop rate of 2%. however they're much easier to obtain by simply purchasing from the moogle shop for 40 munny (32 during bargain flurry) after reaching shop level 2.
you can also buy drop-me-nevers for 100 munny when you reach shop level 5, and find them on drak quack and ducky goose ability link boards. a drop-me-never is twice as effective as a drop-me-not.