Yes, depending on requirements there are a few ways you can implement this. One option is to use Web SQL, which is supported on Blackberry 6.0 +, PlayBook, and BB10. It is deprecated by the W3C, but it is still a valid option if you want to support a large range of devices. If you are only targeting BB10 + devices, then you could use the more modern equivalent called IndexedDB.
There is a great example at http://www.html5rocks.com/en/tutorials/webdatabase
Also check out the BB documentation, if you haven't already. Like the section on storage here:
https://developer.blackberry.com/html5/apis/
Lots of sample code AND it will tell you which devices your DB will work on. Be warned not all storage types work across all devices. My favourite is localstorage but you will also need to assess if you have security concerns.
