The obvious (but not workable) answer is to just charge the actual cost of disposing material in landfills. But this doesn't work because it encourages illegal dumping and littering.
So, I can see two solutions:
(1) Some process that converts bulk garbage into something that takes up less space. Incineration and pyrolysis are like this. Maybe you get some useful energy or gases out of it, but the main point is to reduce the cost of disposal. But this would have to be cheap and clean, a tall order.
(2) A tax on all manufactured goods, based on their disposal footprint, that subsidizes the landfills. Since this tax is already paid it can't be avoided by illegal dumping.