As far as I know, you can't really do this. Shopify doesn't allow pro-rata for apps (even if developers wanted to offer it, they can't).
However, there is a new 'credits' feature that enables app developers to refund money through Shopify. It's been helpful in a couple similar cases for us.
Also, it's important for developers to not allow unlimited free trials for 2+ installs, because then stores could easily uninstall / reinstall every few days, stealing intellectual property from developers.
I'd recommend contacting the app developer and seeing what they can do. Like Ryan said, they might be able to give you a credit.
On a few of my apps I let customers uninstall and reinstall all they want during the trial, their trial dates just get adjusted. But once the trial period is over, there's not much that can be done if they reinstall.