There may be an outside chance if the app is listed in you app history
From the home screen, choose Apps and then choose Play Store.
Choose My apps.
Choose All. (may be Library or History...)
All the apps you have downloaded before but aren’t on your device anymore will be here with a cross next to them.
To re-install, choose the app.
I'm guessing this might work if the app files are still in your phones memory (kind of like restoring from a recycle bin) but I haven't had reason to test this. Do you have "back up my data" turned on in settings?
I can do also install an app from an outside source on my windows phone if I can get hold of an appx file (the mobile equivalent of .exe files for windows) but it can be risky if the source isn't known to you. Android uses apk files. Do you have the app installed on any other device? Or a friend who does? This route is safer if you can get a copy of the apk from a trusted source.
I went to Petguide.com and found the Contact Us page