Please note I've not implemented this myself. I'm merely offering a possible solution..
As far as I'm aware, there's only 2 options you have here. Basic Authentication (always prompt) or it should be possible to install user certificates on the BB devices and use certificate authentication for access to the sharepoint server..
This article might help
http://blogs.msdn.com/zwsong/archive/2010/02/16/how-to-configure-client-certificate-for-sharepoint-authentication.aspx