I need an outdoor flowering plant to cover a railing planter. Suggestions?

Phlox

Also, can’t you just paint the planter to match the rail?

Portulaca or alyssum would work, but they’re both slow growers. Alyssum smells amazing too.

The flowering of Phlox only lasts about 2 weeks. You might want something like Geraniums that last most of the summer and into fall.

If the railing is high enough morning glory would also work. They don’t have to climb, they can trail off the planter.

Yes….^^^^
Morning Glory vines. They are annuals but grow fast have great twiney vines and beautiful flowers. Soak seeds overnight, plant in mostly sun and watch your beanstalks grow. Do not fertilize, they like crappy soil. Keep moist but not wet, it is normal for them to look a little wilted late in the day on hot days. Easy to harvest lots of seeds that store well for next year.
They come in many colors, blues, oinks, purples, striped, white, etc. Easy to grow and impressive but will climb rapidly, up to 7–8-10 feet.

www.youtube.com/watch?v=UKppr2up6mc

Pink geraniums, white petunias, blue lobelia and trailing annual vinca. I used these for a sunny deck for over two decades.

Morning glories are pretty in the morning but then the flowers close.

Where do you live? That would make a difference as to what’s available. I would use something trailing. If I was in the Northwest I would use white lobelia or blue/purple. In many climates, trailing petunias are very nice.

Edit. What I suggested won’t work for those planters! What about some strawberry plants.

Wisteria will twine itself around any nearby supports. It’s colourful, thick, and so hardy that it’s considered an invasive plant in many areas since it’ll choke out everything around it if you don’t prune it back. Plant the wisteria below your planter and let it climb up the railings. It’ll completely cover the planter eventually.