I am with a credit union, and some accounts for children (and even adults) are transactional accounts with no or limited interest rates. If anyone is saving (regardless of a child or adult), they shouldnt be saving in a transactional account, it should be a savings account.
A transactional account is one you link a card to, which has low transaction fees and low interest rate. A savings account is one with high fees (for withdrawing, or linking a card to) and higher interest rate. Thus in a savings account you are rewarded for putting money in, but usually penalised for withdrawing or linking a card to it.
Usually with banks and credit unions, the account with the highest rate and no monthly fees is their online only savings account (cant withdraw from a branch). I wouldnt just look at accounts with "youth" or "child" in the account name.
Once you have a large amount (eg $5000+), I would start to look at term investments with all financial institutions as they can have a higher interest rate than a savings account. I would shop around at each maturity date.