Hi there and welcome to our forum
In general, all you need is sufficient access to the graphics pipeline so you can write data that comes from Coherent UI into the game's surfaces. Client input is very easy, too - we have APIs for mouse/keyboard events so you just convert your input events into Coherent UI input events and everything is taken care of.
I'm not experienced with the Minecraft API (or Minecraft modding at all, for that matter), but from what I gather the mods should be written in Java. We don't have an official port for that platform, so you'll need to take our C++ library and create a Java wrapper. We do have some basic experiments for such wrapper that can render a page and take input (which might be enough for an in-game browser/media player) that we can provide to save you some hours of coding.
So, basically that's it - you need a Java wrapper for our C++ library and access to the graphics pipeline so you can write texture data.