The following is not without risk.
Sometimes, you can fool the iTunes Store into giving you the older version. But there is no guarantee it will work.
If the developer wants to, they can offer older versions of an app for download from the Purchased tab. This means you have to already have downloaded/purchased the app. And it only works when you try to download the app on the older device.
If you purchase an app from the iTunes Store on the computer, it does not filter by iOS version. That means you can download just about anything you want, whether your device will run it or not. Once you've done this, you can go to the Purchased tab on your iOS device and try to download it from there. If an older version is available, it should be offered.
For various reasons this does not always work. It's probably worth trying for free apps. Not much to lose there. But if you're looking at a paid app you could easily end up paying for nothing.
Hold in mind that if it does work, you are still getting an older version of the app. It may look different and lack many of the features advertised for the newest version.