You might check Oracle HTML DB and see if it suits your needs. Download page is here (for MS Windows version; navigate through Oracle Technology Network pages to find more about this product and/or other platforms).
Usually all the Web hosting providers suggest MySQL or PostgreSQL (not Oracle). One day ago I have found two services http://www.freesql.org/ and http://www.smansh.com/en/. The first is free but does not work normally, a lot of bugs (betta). The second seems simpler (no SQL) and works better. While, I tested only Trial (free) version.