I wonder whether any of the available downloadable images have Java support built in - maybe the Debian* one?
If you need to have Java support on a Yocto* build my blog might be of interest for you:
https://software.intel.com/en-us/blogs/2014/04/04/some-hints-on-yocto-builds-for-iot-devkit-example-... Some hints on Yocto builds for IoT devkit - example: adding Java JRE
There's at least one place I know of - folks from Intel-NTU Connected Context Computing Center in Taiwan have created a set of images (I think based on 0.7.5 BSP) with various JDK and Tomcat versions.
See here: http://ccc.ntu.edu.tw/index.php/news/40 Intel-NTU Connected Context Computing Center