Mod podge will work!
Have you tried spray adhesive?
3m SUPER 77 or the 93 whatever is highest number by 3M will cover your pail you want to leave the fabric as big as you can and trim it after you wrap the sides all the way up
How about contact paper?
You could use mod podge but it won't be waterproof after.
I'd use Mod Podge.
I would use spray adhesive and a glue gun. Measure the size of the ice cream pail all the way around and cut your fabric to that size.