Keeping testers busy tends to get easier as a project matures (there is more to test!), but the following points apply in the early stages too:
Testers can prepare their test plans, test cases, and automated tests for the user stories before (or while) they are implemented. This helps the team discover any inconsistency or ambiguity in the user stories even before the developers write any code.
In my personal experience, testers don't have any involvement in unit testing; they only test code that passes all of the automated unit, integration and acceptance tests, which are all written by the developers. This split may be different elsewhere, though; for example your testers could be writing automated acceptance tests. Unit tests really should be written by the developers, however, as they are written in tandem with the code.
Their workload will vary between sprints, but regression tests still need to be run on these changes...
You may also find that having the testers spend the first couple of days of each sprint testing the tasks from the previous sprint may help, however I think it's better to get them to nail down the things that the developers are going to be working on by writing their test plans.
