Again, the plastics used in most all hard sided coolers are polypropylene and polyethylene. By their very nature they are hard to bond to using just about any adhesive. That one of their benefits for their use in applications for things like coolers and storage containers - $#it don't stick so its easy to clean, hard to stain, slickery (technical term meaning slick and slippery).
Bonding these materials to other materials and even to themselves is difficult. Bonding them to themselves typically require them to be welded - heat up the mating surfaces and smoosh them together (smoosh is another technical term meaning... smoosh).
They are not like PVC where you can put on a primer and PVC glue. These are solvents that chemically soften the skin of substrate and the bonding happens by mushing or smooshing the two parts together and waiting for the solvent to evaporate.
There are some primers out there that can be used to prep the surface of polypropylene and polyethylene prior to applying the SuperGlue but I haven't had much luck with this combo for long term adhesion. If my suggestions of physically roughing up the surface to give it some "tooth" so the adhesive has places to key into don't work for you (again, I haven't had much luck for long term adhesion this way either), you could always try what industries use for surface prep: flame, corona, or plasma treatment. It'd cost a few thousands of bucks for the equipment though.
Here's a little sumptin', supmptin' on methods of bonding to polypropylene and polyethylene.
https://www.permabond.com/resource-center/comparing-flame-corona-plasma-treatment/
If that didn't answer your question, then I don't know what to tell you.
In summary, best bet is to skuff up the surface and try Super glue or two sided sticky tape. I'd go with the two sided sticky tape, the Super glue might ruin the cigar bands.