Reddit reviews Bird Coloration, Volume 2: Function and Evolution

What you're looking for is "reversed sexual dichromatism", aka females more colorful/brighter than males. It's a subcategory of reversed sexual dimorphism. It occurs in phalaropes, some other sandpipers (Eurasian dotterel and some plovers), button quail, Eclectus parrot, belted kingfisher and fairy wren (though the fairy wrens have an odd situation in which there are 2 forms of males: some extremely plain and dull, and some very brightly colored, and females in between). All of which have been studied fairly intensively because it's so unusual. Most of these species also have "sex-role reversal", e.g. female is more aggressive, female has multiple mates, male does all the parental care. But the eclectus parrot has does not have sex role reversal, which won it its very own Science article. It appears the eclectus females have violent battles over nest-holes and will even kill each other over nest-site access, which seems to have exerted pressure for dramatic coloration for intra-sexual aggression; and because females can retreat to nest-holes in case of predators while males cannot, the males seem to have been under selection for more muted coloration as an anti-predator defense, while females have not.

Anyway, in some cases the female's brighter coloration is quite subtle (like the dotterel, here) but when you're close up to those birds it's actually pretty noticeable. The pharalopes and belted kingfisher are more obvious (scroll down in that link to see the female vs male red phalarope - the female is entirely red, male is kind of scruffy looking, pretty dramatic. The female's actually brighter red than it looks in that pic - it's shadowed in the pic - but I could not find another site that had side-by-side female and male pics). In a few cases it is pretty dramatic - the eclectus parrot is probably the most extreme case and was thought originally to be 2 different species because the sexes look so different.

For most North American redditors, kingfishers are the most common case you'll see. There's only 1 kind of kingfisher in most of North America, the belted, they're in a lot of highly urban ponds/lakes, they sit right up where you can see them, and only the female has the red bellyband. So next time you hear that rattling call when you are walking around a pond, look and see if it's got the red bellyband (= female) or not (= male). They're fun birds to watch anyway. (non-NA'ers, sorry, go find a dotterel I guess, and you lucky Australians can go feast your eyes on the eclectus!)

Ref, also see the chapter on females in "Bird coloration" though unfortunately you can't get that chapter online.