What type of UV-resistant (fade-resistant) paint is best for a rain barrel made of polyethylene? It will be in a greenhouse
“Adhere to polyethylene” is going to be your problem. It Does Not Like things sticking to it.
I suppose you could voraciously scuff-sand to create a surface with a lot of “tooth”, then paint it in epoxy, hoping for a mechanical bind.  Ideally epoxy primer like Amercote, but that is too dangerous for consumers to use. I suppose something like West System 105 would do.  Sunlight will quickly destroy the epoxy, so you’ll need to topcoat it with something.  But paints stick a great deal better to epoxy then to polyethylene.