Hi Lauren! Nice to meet a fellow islander on this forum
I am only familiar with a few species, so someone with more experience will hopefully chirp in. However, off the bat I would rule out for you eclectus and lorikeets. Eclectus because I've read they have a tendency to stress plucking and I feel like a house full of reptiles would perhaps be stressful for them, lorikeets because they're really messy due to a nectar diet and with two young kids, you probably don't want to add to that
As you've handled conures before maybe you could consider one again? Particularly a bigger, more robust subspecies that handles kids well? You might also consider a caique?
Nice to see you on here too

I think eclectus may be a big big for us - they are stunning birds however if they did bite they might remove a finger on my kids

. I am thinking a conure might be a good idea - particularly the Pyrrhura species. I love caiques - however I have read they can get quite nasty when they hit 'puberty' - is this right?
IMO cockatiels do great with kids. My cockatiel will go to anyone and my little cousin who is 5 can handle her and my cockatiel doesnt even mind. A couple other species is Princess of Whales parrakeet(they are on the larger size of the parakeets) and a Kakariki. These are both very gentle and typically the females are more gentle and if you plan to add another bird these will be less terratorial.
I don't really want a cockatiel, as lovely as they are I would prefer something a little more unusual in looks. I haven't seen Princess of Wales as hand-reared over here so I ma not sure on the availability of them
Of course, I am partial to Eclectus parrots and in your case, I would suggest a male because thay are more docile than the female. They also seem to love everyone in the household but may lean towards you a just a bit more if you are the sole caregiver. Regardless, they are known for their gentleness with children. The other thing to consider though is that they have strick diet, so you must moniter everything your kids might feed him/her. We had an Yellow-Naped Amazon before (which is a good species) but he seemed to more partial to me, but we got him at an older age from a male owner, so that could be a reason. Otherwise, those are the 2 breeds I suggest... They are both talking breeds, especially the Eclectus. You said it doesn't matter but I think your kids would enjoy teaching him to say fun things and cool songs. It may pay off to consider a more talkative breed to bring your family together even more!

Good luck on your search! I'm sure you'll find exactly what you need for your family!
I think I've ruled out eclectus because of their size - they are so pretty but not for us. I do like Amazon's - I used to have an orange wing rescue - she was gorgeous but I had her long before my kids. I might consider an Amazon again but that would be the biggest species I would consider.
A couple other species is Princess of Whales parrakeet(they are on the larger size of the parakeets) and a Kakariki. These are both very gentle and typically the females are more gentle and if you plan to add another bird these will be less terratorial.
My mom has a male Princess of Wales. He talks, is cute, funny, and active, but IMHO they are best as aviary birds. The aviary lifestyle goes along better with their natural characteristics. Shows off their tails too. Over twice as long as the body!
Is there any characteristic or traits, or size of bird you might be thinking of? Let us know some specifics that might aid us in helping suggest for you

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I will certainly look into hand-reared Princess of Wales - they are very pretty birds but I am not sure of the availability of them . They sound really nice though however if they are more suited to an aviary then I would have to consider that - I will certainly do some research on them. I don't know much about kakarikis - I will look into them in more detail
Parrots are usually not very well suited with homes with little kids, but you can always give it a try since you have experience. I'm not any expert on birds and kids, but I think cockatiels and/or budgies should be good choice. I would avoid any bird that can bite hard or get aggressive. It's a big difference if you are getting a bird for yourself or for your kids.
My kids are quite sensible and are very good with animals - my 4 year old daughter is allowed to handle (under supervision) my crested geckos and she does this very gently and with great care, she is quiet and calm around them.
I have also added at the bottom of this that really the bird will be mine but would have to tolerate the kids.
I just re-read your post, and I'm thinking that maybe a young hand fed Budgie or two would be perfect for your kids to learn about keeping and handling birds. Is that a little smaller than you were hoping for?
Budgies are very cute in their antics, and besides the screaming, they make cute little sounds that always make me smile. I've had parrots for years, but got my first Budgie less than 2 years ago. He's not handleable, but I love him all the same. I bet a super tame hand fed would be an adorable and wonderful little pet. I'm not sure if you commonly have both types where you live? English and the smaller American?
That's my suggestion

good luck whatever you decide.
I used to have budgies as a kid myself, I love them but I wanted to get something a bit larger - I was thinking a minimum of a Pyrrhura conure size tbh.
Thanks to everyone who has replied

I should have added more details on the original post. I would prefer something a bit more unusual than a budgerigar or cockatiel - these are lovely birds though. The parrot/parakeet would be cared for by me predominantly however it would have to tolerate the kids and interact with them without freaking out or attacking them. I know a lot of the larger parrots tend to bond with one person which wouldn't be right for us. I would only be buying a hand-reared bird as I feel that would be better for us, especially if it has been brought up in an environment with kids already.
My kids are good and well behaved however they would not be allowed to be getting the bird out without supervision. Size-wise somewhere between a Pyrrhura conure and an Amazon would be ideal. I have posted this on a UK forum as well and had suggestions on there as well - it is such a hard decision!
The species I have been suggested on there have been:
Green cheeked conures, ringneck parakeets, quakers, caiques, Pionus species, Australian king parrots, Senegals and Meyers.
I have been looking at videos on YouTube and reading on websites and I think I like the sound of a ringneck, caique or another conure - has anybody got any reasons why these wouldn't be suitable for me and my family? I would rather have honest opinions than just reading the 'rose tinted glasses' versions that YouTube and some websites portray. I will certainly consider the species I have been suggested on here though and do my research carefully before purchasing any bird as I know this is a lifelong decision and needs to be 100% right.