BoL clearly explains what can be done:
Permissions
The minimum permission required is ALTER on table_name. TRUNCATE TABLE permissions default to the table owner, members of the sysadmin fixed server role, and the db_owner and db_ddladmin fixed database roles, and are not transferable. However, you can incorporate the TRUNCATE TABLE statement within a module, such as a stored procedure, and grant appropriate permissions to the module using the EXECUTE AS clause.
So, you have two choices:
Grant users ALTER permission OR Create stored procedures (with EXECUTE AS) which will truncate specific tables and give users permission to execute these procs.
Just one more idea: You can create SQL script/proc which will auto generate such stored procedures for the required tables.