Dropping rhymes with:
cropping, propping, chopping, copping, cropping, flopping, hopping, lopping, mopping, popping, propping, shopping, sopping, stopping, swapping, topping, wapping, whopping
Dropping sounds like:
deriving, drabinsky, draping, drepung, dripping, driving, drooping, droppings, drubbing, dwarfing