Opening a savings account having delinquent payments

You shouldn't have any problem opening a savings account. Banks are more interested in checking your credit for a checking account. Since it is pretty much impossible to take out more money than you have in a savings account, you shouldn't have a problem.

You should be fine. If the big chain banks would turn you down, most of the smaller banks will approve you, too.

I didn't have any problems opening up an account.

Caution: don't tell anyone you've got the savings acct., or what bank you use. Cash your paychecks at the bank they're drawn on if you can. If someone has or obtains a judgment against you, they can do a writ of execution and garnishment to have your savings account seized without prior notice to you. Then you'd be in the position of having to go to court to explain why they shouldn't be allowed to do that. Better off not to tell anyone about it. If you live near the state line, you might do well to get your account at a bank in the neighboring state (not just a branch of the same bank that is in your state, that can still be garnished. you need an out of state bank that will be immune from service of process in your home state.)