I am not sure what material the buckets are made of but if they are of the soft vinyl (like many waste baskets and mop buckets): Rough the surface with steel wool or sandpaper and spray with a primer. (You can use a brush primer but that is much harder to get a smooth finish) Numerous light coats so it doesn't drip! You can then paint with any latex or acrylic paint. Many companies now produce stencils (try a search engine) for faster production or buy some tubes of acrylic art paints. You should then apply a clear coat (urethane) to protect the design.
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