We just heard that SlingMedia is putting out a beta of SlingPlayer Mobile for BlackBerry on December 30.
Only AT&T and T-Mobile BlackBerry devices with WI-FI and the BlackBerry Bold are supported according to the Sling Player Mobile for BlackBerry Beta site, however, I am sure that someone is going to try to get this to work on a Verizon and Sprint BlackBerrys as they have pretty speedy connections.