I have a paid app in the Play Store (Profile Widget, in case anyone is wondering ;)) and I want to allow some users (friends, or people who do not have a credit card) to dow
this is an updated and no credit card method.
You can create a free version of the same app in the play store, but publish it in alpha release. Then, you can create a google+ provate group of alpha testers and set it as the tester group for the alpha version.
Now add the 'free licensed' users to the alpha testing group and they have your free app.
To push updates, you will have to upload updates also to the 'free alpha', that's not gold, but I think is pretty close to the best you can get at the moment
This method has an issue. As long as licensing is per-App, you will have a different license key, and it may always return TRUE, so if the users share the apks, they may be able to let other people use the app, not totally sure about this occurrence, but you are warned, better if you are sharing the free app to trusted users.