Millet is the first thing that comes to mind, especially ornamental varieties like 'Purple Majesty' and 'Purple Jester'. Similarly, there are some varieties of corn that might be suitable -- look into popcorn varieties (there's one with cobs that resemble strawberries) or ones used for "baby corn." Can parakeets eat amaranth seeds? What about Celosia? ornamental grasses? Echinacea, Heliopsis, Sunflowers... Trying to think of other plants I've seen birds noshing from at the end of the season.. I know that the seeds being edible doesn't mean the whole plant is safe, but it seems like a reasonable starting point.
For perching, how about some of the newer Crepe Myrtle cultivars, with purple foliage and bright blooms? Many of the new ones are compact, too, including some true dwarf varieties. I know the goldfinches in our yard love the seeds, but you might want to check into whether the leaves are parakeet-safe. I think people can eat hibiscus blooms; are they on the list of safe plants for 'keets?
interesting question! I'm looking forward to seeing what folks come up with...