For the deploy part you can use phonegap (now called Cordova). It is an Open Source library that pt provides a framework to create "native" mobile applications using only web tecnology (HTML5, CSS3, etc)
It has two parts:
That way, you can build a "native" application which is in reality a web view that loads an URL to your local data.
So now your question is hopefully reduced to just selecting and testing an HTML game engine / library. Unfortunately I can not help you with that as I've never use HTML5 to create games (yet) but to get you started, here you have two HTML5 engines:
Beware of performance though, it varies a lot even between different OS versions.