Harrison Library has most of the Diocesan Journals for the Diocese of Texas in its non-circulating collection. These journals are in-library use only. A few of the older volumes are stored in the library's Special Collections room, where the temperature and humidity levels are carefully controlled to preserve fragile print materials. You will need to reach out to the librarians to access those volumes.
There are also a number of journals freely available online at HathiTrust.