I have 4 young kids that each have a piggy bank for collecting coins and putting their allowance in. When the banks are full we take them to the bank and deposit them in their accounts, usually around twice a year.
Encourage your child to save half of any money that they receive, whether it is from their allowance or a gift. Work with them on how they would like to save the money.
I have this coconut bear coinbank which I got four years ago. This was a freebie from opening a kiddie bank account for my child. The bank gave this to encourage parents to teach children to keep at least a single penny a day.