Because June 11 sometimes happens in the Easter Season, you can read in TDP about St. Barnabas both on pg. 421-2 and 1302-3. Also an old Aardvark Alley post has this.
And you can (sort of) join in the corporate worship of God in thanksgiving for this Apostle by listening to the chapel service at the Ft. Wayne seminary. (Under the "Online Giving" paragraph, click on "Thursday 06/11/2009" in the tool.)