A close relative, the King Parrot, is probably more readily available and more common to get a hold of than the Red Wings... that said, I don't know how common they are outside of Australia. I do know someone who had kept King Parrots years ago as pets and enjoyed them!
Although not related, another possible bird to consider would be the Princess Parrot. Far more common around the world if you can find a good breeder, but still kind of rare.
I've never seen a captive or "pet" red-winged parrot, probably because they are not commonly bred in the US, and as Monica said, they may not even exist outside of their native Australia. King parrots I have seen, but very few...It's not that these birds are "not intelligent", pretty much ALL birds are very intelligent, from sparrows and robins to parrots to dove and pigeons to hawks and raptors to penguins, they are all very intelligent. However, not all birds/parrots make good pets, and some species of birds don't do well at all in captivity. It's no different than a lot of breeds of cats and dogs; there are many wild breeds of both cats and dogs that have never been bred into captivity to become pets, as they just wouldn't make good pets...For example, you don't see many Dingo's living in houses as pet dogs. Could they be bred into captivity and domesticated? Probably, but over decades to centuries.
***I'm assuming that Monica was referring to a Princess of Wales Parrot/Parakeet when she mentioned a "Princess Parrot", and it was a great suggestion if you are attracted to the Red-Winged Parrots, because not only are they gorgeous parrots, but they make wonderful pet birds! My mother bred them for years, and they were some of the sweetest, most loving birds I've ever had the pleasure of living with. And they are not louder than any other parrot. They are pretty common as pets, and you should be able to find a Princess of Wales Parakeet breeder online at websites like
www.birdbreeders.com and
www.birdsnow.com
The other species of parrot that is also related and that make absolutely wonderful pet parrots are the Canary-Winged Parakeets, also called a BeBe Parrot/Parakeet. They are extremely intelligent, not at all loud, can learn to talk very well, and most of all they are some of the most loving companion parrots period. Just like the Princess of Wales Parakeets, the Canary-Winged Parakeets form very close bonds with their people, and just love to be with their person, snuggling and playing. And again, they are very commonly bred in the US...I actually was shocked to see a hand-fed baby Canary-Winged Parakeet at a Petco in Altoona, PA not that long ago. I had driven over there because my local Petco was out of the calcium/multi-vitamin I give my Bearded Dragon (it's 25 minutes from State College), and it's a much newer and larger Petco that the one in State College, like easily twice the size, so I always look around when I'm there...They had multiple Green Cheeks, Suns, and Jenday Conures, along with a Cockatiel and of course Budgies, and when I turned a corner, there he was, a little green, baby BeBe Parakeet...He was horribly overpriced, but adorable. So they are obviously becoming more and more popular.
I doubt most people could remember the latin name for their own bird, let alone a latin name for all the other species! LOL 
Which actually got me thinking... We have "King Parrots", "Queen Parrots" (Queen of Bavaria/Golden Conures) and "Princess Parrots".... but no 'Prince Parrot'? Or what about a 'Joker Parrot' or a 'Knight Parrot'? I mean, there is a Night Parrot, but not a Knight Parrot, ya know? 
