If your company already has Blackberry Enterprise Server (BES), there is a chance that it will work with your task list. BES is a very reliable synchronization platform if you task list supports it. Check with the task list publisher about BES support.
Otherwise, see if Blackberry Desktop supports your task list (Lotus Notes is supported, for example). If so, use it to sync manually. Point your browser to na.blackberry.com/eng/services/desktop/ for the latest version. This application can sync your Blackberry when you connect it to your computer. It even lets you choose which tasks to keep up to date.
Some Blackberry apps sync to desktop and online task lists. See Priacta’s list of TRO-capable apps at stg.priacta.com/gtd#tro. You may need to search the page for the exact device name/type (e.g, Storm).
You can also do TRO without a syncing smartphone. If you ever work away from your desk, print out your Do Today list, make notes on it, and process the changes each day. Some people love this. Look for a task list that has a tolerable print format.
You can also use your Blackberry calendar to see a mobile Do Today list away from the office, no syncing required.