Hypersonic is capable of supporting small databases if you are happy with that. You will probably want the support tools to create and manage the databases other than from JDBC. Check the SourceForge entry and get the package and the documentation and you should be away. Just read through the webdocs to get an idea of whether it is suitable for your needs and what mode you want - probably file rather than all in memory. The utilities will also help you backup the data.
See http://hsqldb.sourceforge.net/ for more information.