Simple rail & hooks solution to attach a bin to the inside of a cupboard
Almost all plastic trash bins have a turned over lip around the top. Why not make a French cleat slightly narrower than the width of the bin and hang the bin by its lip on the cleat?



A French cleat is a long narrow board whose front edge is higher than its back edge. A mating board with the reverse configuration is then hung on it. In this case, the bin lip is the mating piece.

You could use a small rotating clip, such as a plastic mirror clip, to keep the bin from bouncing off the cleat. Just don't tighten the retaining screw too much.