If you google it, many will come up. Some especially for children or are adjustable to fit a child. One pair is in your price range. The problem I had when I was searching for them is that noise cancelling headphones generally are ones for a CD player. I only wanted headphones to cancel noise for dd.
So I found that. These headphones have no cords, are adjustable to fit adult or child's head, and are lightweight. What I didn't realize is that they do not cancel out noise as well as I thought. I thought it would silence loud noises like fireworks. I don't know? I was a little disappointed in these. My dd could very well not use them and it would be the same? Cost I believe $35. These are going to probably stay on top of the dryer where they have been for ages. These are not breakable though--as they have come apart and easily fit back together again!
Anyway my suggestion is to get the higher priced ones that go with a CD player. The ones I have are wonderful. Sounds are so muted as not to bother my daughter. I put on music for her that she enjoys and she doesn't jump out of her skin over sounds any more at fireworks, etc.

I told myself since these headphones cost so much, that they would last longer than the cheap ones anyway.

Cost about $150. These are the ones going with us on our trip. I have been loading Disney songs for dd for a week! I don't know about them being breakable as I don't let dd wear them unless under supervision since it has a cord to it.
Also before you spend the money, if your child does not like wearing hats, he may not want to wear them. No way my dd would wear earplugs!