Do you know of safe ways for my young children to interact with our pet bird?

Answers:
supervision is key!!! i have a slightly aggressive blue crown conure, and although he is OK with us, he will hurt what he considers strangers. my kids are ages 3,4, and 8 and they are only allowed to pet him while he is with us and far away from his cage. he climbs on their head, preens them but i also noticed that if he is not in a playful mood he will bite them. my 8 year old got bit but not hard,more of a "get away" nip, because she wants to PET him all the time and he is more of a loner. if we put him on the floor he is nice to anyone who will save him, and he completely understands when we say "paulie, dont you dare" and backs off. it would help to know what kind of bird you have and what he is like. i have lovebirds as well and my kids handle them all the time, even the ones that bite. again, supervision will save them a lot of pain and with time and patience, they will be able to interact with your bird.
ps- my kids constantly give paulie treats, and they are responsible for his water which has helped their relationship quite a bit.

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Under supervision. Your children require you to teach them to be gentle and never to pick up your bird. Start by getting your children to assist you with caring for the bird like cleaning the cage and changing the food and water daily. As they help you explain the significance of doing these chores for your bird. Young children should never be aloud to interact unsupervised with animals, for both theirs and the animals safety.
If you start now while your children are young and actively teach them about the bird (maybe ask your children to help you find books on birds at the library and then read them together as a start) they will see that you respect the bird and care for it and will learn to be responsible young people.

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You did not mention how old your children were and what type of bird you have. My son is almost 7 years old but has ADHD so although my pet Eclectus parrot knows him very well, he makes my bird nervous.
It really depends on the character of your children. I've seen younger children do very well with pet birds because they are by nature calmer and more gentle. It also depends on the type of bird you have. A friend of mine has an adorable pet cockatoo who simply would not suffer to be around children. Meanwhile my other pet bird is a pet Greater Indian Hill Mynah who thinks he rules the house and hops onto everyone and simply flutters away when the kids scream in panic, then comes back for more. So it could depend a lot on the type of bird you have too. A smaller bird could possibly get hurt whereas a big bird could inflict quite some damage on your children if provoked.
Indeed, the simplest answer would be 'close supervision'. If your children do not look ready, wait a while. A good introduction could mean a life-long love for pets or an eternal phobia (for both the bird and children). Keep their interactions very short (5 minutes max) each time and gradually extend their playtime together. But do not expect anything more than 15-20 minutes.