I am not sure about a specific API, but AppBrain could "push" apps from the web to your phone before the most recent Market release (the one where they updated the market app on the phone). After that, this functionality was broken, and AppBrain said it was due to changes Google made to the market.
Now, push installs from the web are available in the market released today. Here is the comment from AppBrain (directly from the listing for their app Fast Web Installer): Recent changes: Please note: Google disabled fast web installer in the newest version of Android market (2.12). -- You received this message because you are subscribed to the Google Groups "Android Discuss" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/android-discuss?hl=en.
