This should be achievable using our Yocto Project / OpenEmbedded-Core build system, although JREs tend to be rather large. You can either start with the “console-trdx-image” image recipe and widdle away unnecessary packages or you can build the “core-image-minimal” image recipe.
I recommend viewing these webinars related to the build system (although they don’t cover everything you need to do to meet your needs):
Building of core-image-minimal will require using a different distro called Poky - use of Poky is covered by an article at our blog.
You might also view this webinar about optimizing boot time which discusses building a very minimal image.
Which JRE do you plan to use? OpenJDK JREs available through meta-java are probably ~35MB or so. Its a little harder to say with Oracle JREs - the full Java SE JREs from Oracle are probably similarly sized; although smaller Java Embedded JREs can be generated. Size optimization should be possible with either of these options. There are 3rd party embedded ARM JREs as well.