RUNS on 256mb ram
and has java in the app store [I think]
The best thing is to do some research on here and balance between lightweight and the amount of support you can get. Some have better support than others. Let us know how this turns out please.
For anyone looking into it, I've found out that, though it is buggy, the best OS with support , but is lightweight would be Lubuntu, if it is run from a hard drive. If its run from a USB stick, unless you are able to allow ubuntu to boot from RAM every time, which is complicated, Macpup/puppy linux is the best of all. They run very fast, even when on a USB stick, and there still are some computers in which the graphics run well on. I was sustaining 22 fps in Minecraft with smooth lighting on an old laptop wiith 512 Mb of ddr RAM, and something like a 700 mhz processor!! That goes to show how If you can get the drivers working, Macpup is the best. otherwise, Lubuntu has more support (But for the most part, must be run on a hard drive).