if you want to be neat, lime pit or hard wood ashes (deep pit and sprinkle liberally). if you live near a salt deposit you could mummify them. pile them into a designated empty house - burn when full.
if you want expedience and still keep the smell and possible disease load down;
ocean/beach dump or find someplace nearby with vultures or coyotes. Sky Burial anyone?
most eco-systems have similar critters. New York it might be rats and feral dogs.
stack and inoculate with rid-ex and sour milk to jump-start the process. Stay well away for at least a few months.
if bodies pile up faster than that will accommodate - endure it? realize you will never wash that smell out of your hair or clothes?
I think a worse case is if the infrastructure collapses without removing alot of the population.
dead bodies might disappear on their own after a month or two of hunger and fear.
dragging them to a river is like dumping them in the ocean - you might poison your neighbor. If food is short where do you get the calories, manpower and as you mentioned time to play undertaker?
... i hear there are a bunch of empty wallymarts around - turn them into a shrine for our departed brethren?