Hey Erglmop,
just quickly: There is currently no official way to do this properly. And security is not really the right place to use shortcuts. Right now, asking the user for his or her credentials seems the best way to me.
Ok, here is the long story:
There is two qualities to that: convenience and security.
For convenience reasons it would be great if you wouldn't have to provide your Google credentials to the apps separately. But even from the convenience point of view this is only (a little) convenient to some and very inconvenient to others. There are users that don't want to use the same account for the phone (e.g. gmail) and for their Google Reader account. This is very often the case for users of Google Apps for your Domain users.
There is some "pragmatic" solution used by some programmers, but it is nothing official and doesn't significantly improve security. I decided that the little convenience gain you can get with that solution is not worth going down a slippery slope.
Regarding security. An ideal solution would be that NewsRob fires an intent that it wan't to access the Google Reader part of your Google account and a Google app answers that intent (that's the cross-app re-use mechanism on Android), verifies it, asks the user to grant the permission to NewsRob and then returns an authentification-token that authorizes NewsRob to only use the Google Reader part of your account.
Ideally the Google app would let you chose between the phone's identity and other Google accounts you may have, but I would already be happy without that.
If there would be a proper solution from Google I would implement it right away.
Btw. for me this is not an ideal situation too. This issue comes up regularly, I get bad ratings and had to implement my own login mechanism that doesn't add any NewsRob-value to the app.
I hope you understand and star the bug report from above, not that I am holding my breath for Google to act on it right away.
Cheers,
Mariano