WWcC,
As Retired mentioned Standard Chartered do have a Dream Account - but the special offer for children has elapsed. It's just a normal account now.
You won't get higher savings rates for children's savings accounts in Hong Kong but there are a number of banks that do offer children's savings accounts. They're not your main big banks so check on their branch locations.
In no particular order, the one's I know about (there may be others) are:
MEVAS Bank
Read More
Fubon Bank
Read More
Dah Sing Bank
Read More
Dah Sing Bank says: "To encourage kids to save, Dah Sing Bank offers a special Award Plan and grants extra incentives to children who develop a habit of saving. Details will be notified individually." Got no ideas what those details might be but MEVAS Bank are known for generally offering higher interest rates.
By the way don't buy a children's education savings plan which they might try selling you while you're opening the savings account for your child. The rates of return are pretty low and there's better ways to save for your kid's education.