After receiving your child's Entertainment Work Permit (if you have not done that, then go to my Ehow article on How to obtain an Entertainment Work Permit) your child is now eligible to accept work.
Some financial institution need you need to show proof of employment before they will set up an account some do not. For those with principal or speaking roles contracts can be used to show proof of employment. For those with background roles you must first complete a day of work and use your voucher receipt as proof of employment.
Coogan accounts should be obtained within 90 days of employment or it goes to The Actors' Fund of America as the trustee of unclaimed Coogan funds after 180 days where they hold the money in trust until it is claimed.
Not all financial institutes "do" Coogan Accounts. You need to search on the internet or call. If you ask them and they do not know what a Coogan Account is, then just call the next bank on your list.
Keep in mind that you will not be going to the bank until your child is 18. Picking an institution in Hollywood such as First Entertainment Credit Union (if you are in Southern California) is a good choice. They have been dealing with Coogan accountants for many years and will do everything via mail.