Actually you can do this. Apologies, I know it's an ages old thread but it still comes up in searches.
You have to have had the App when it was available in the iOS version you are trying to install to.
When you try to install it, App Store will say something of the lines that this app requires iOS8 (or 10, currently) BUT it gives you the option to install the older version. I have just put an old version of Find Friends on an iPhone 4 running iOS7 which I'm setting up for my daughter.
Incidentally I had to go into settings and sign into iTunes & App Store with my own AppleID on which the earlier "purchase" (ok, it was free) of the app had been made. Then after the install go back into settings/iTunes & App Store, and sign back in with my daughter's account.