I tried to locate second chance banks and fresh start banks in the state of Rhode Island but I was unable to find any. However this does not mean that they don't exist so I would suggest calling your local credit unions in your area to see if they can help out with opening a checking account.
You can also use one of our nationwide banks at http://infoaviator.org/finance/checking-accounts/2014/05/28/how-to-open-a-second-chance-checking/
. They may not have any branches in your area but you can still open a account with one of the larger banks and use direct deposit if you have that.