Well, there's App Admin, which is a jailbreak tweak.
But the option to download an older version is a stock Apple feature. But it is dependent on the developer.
If the dev leaves a version for that iOS on Apple's servers AND if it is an app you have downloaded at least ONCE in the past (no matter how long ago) you SHOULD be presented with this option.
Apple even lets you continue to download apps that you have downloaded in the past when they are no longer in the app store.
If you have never downloaded the app though you are out of luck.
I have at least one app I downloaded in the past that's not available on the app store anymore.