how can I download older versions of app. I only have 5.1 ios

How can I download an older version of apps. needing a 6.0 ios? I am going crazy. I got this ipod from a friend and she doesn't remeber her password. So, I backed up her apps.Then restored the ipod. Now I can't reinstall the backed up apps because of the password problem. So stupidly, I restored it to the original version. Now, I can not install any of the apps my son had on it because of it being a 5.1.1 ios. What can I do? I have also already put money into my itunes account onto that ipod. and I think it is rediculous that there isn'y an option for an older version. Is there. Please help.