I am looking to glue some vinyl tablecloth material (the type you can buy anywhere in France as it is waterproof and usually left out on garden tables) to a plastic swing bin. Does anyone know which adhesives are best to use for this?
I recommend using plumbing silicon (not acrylic) from a tube, the kind that is used to seal the gap between a sink and porcelain tiles. It will remain flexible and if you spread it evenly it will stick pretty much forever. It is also quite cheap and waterproof - one tube should be enough for you.
Lay your vinyl sheet on the bin, mark it and cut it to shape before you glue. Press out long lines on your bin, smear them flat with a tool and place the middle of your sheet on the bin - working outwards. Let cure for 24 hours.
At work we work with several different plastics, mostly in sheets, and vinyl is one of them. I found that most sticky tapes do stick to vinyl, often when you do not want it. They will usually also stick to the backside of the vinyl used for tablecloths.
The glue used for sticky tapes comes in many different strengths and you can get it in different ways. For indoor use most tape glues will work, although water is about the only thing that makes the bonding weak. For outdoor use and for very wet bathrooms I would go for a very strong or waterproof tape-glue.
In your case I would look for a double sided tape or a 'tape free' sticky tape which can be found in dispensers. Craft shops and craft sections of the cheaper shops ('everything €1') often stock several versions as do shops for office supplies.
If you have the options, I would go for 'permanent' rather than 'undo and stick again'.
If you can not find double sided tape, you can use normal sticky tape, folded double or into a tube, with the sticky side out.
The 4 or 5 cm wide versions are good for this but narrower tape will work.
A tube made of a spiral works very well but it takes some practis to get it evenly and long.
Do test the fabric and the bin to see that the tape does take to it.