I'm about to bring a 3$ app to the Android market. To get reviews and for promotion I'd like to give out coupon codes for a free download.
Is there such a feature build in the Android market or are there better ways to do it?
Google Play does not seem to have the coupon feature. I'd suggest considering a free app (basic features) with the option to unlock power features with in-app purchases. The method is simpler for the end user (no coupons, download the app straight away), and allows them to test-ride the app before making the purchasing decision. At the same time, the app is downloaded through Google Play, thus increasing your chances of getting rated.
As a side note, the mobile app market is rapidly moving towards free apps with in-app billing enabled. You might as well benefit by riding the initial wave. Data suggests that an average user who chooses to spend money on in-app purchases spends $14 per transaction on average (Flurry, 2011 ).
There is no such option in the Android market.
You might want to distribute the apk file by yourself, but I am not sure if it is possible to update the app through the market if you haven't paid for it.
Send bloggers an apk with all the features unlocked. If they review apps this should be standard for them.
Another option would be to start with the app being free, but without promoting it or even giving it a meaningful title on Google Play. Give the bloggers the link, set up a don't-publish-before date (and hope they honor it), and make your app payed and with proper marketing material before this date.
A final tweak could be to have it free but require a "beta code" to activate.