Not sure who records or archives news radio in the Dallas-Ft. Worth, Texas metroplex area, but I am looking for the news casts from those dates (would also be interested into TV news casts as well). The two major Dallas news radio stations at that time were KLIF and KRLD
There is no formal entity that records and archives radio newscasts.
Back in 1991, we were still in the tape recording era. Even at slow logging speed, you needed a bunch of those big reels for every day. Overall tape cost for a month might have been well over $1,000. So tapes were recycled often.
While computer hard drives and music recording software existed, it was way too expensive to record and save newscasts for individual stations. Those were the days when a 200gb hard drive was around $300 to $400 and recording equipment was relatively costly.
Some stations recorded and kept those recordings for enough time to verify commercials were run. Then the tapes were generally reused. Again, cost and the huge amount of storage space needed made reuse essential...
Smaller stations did not record. Larger ones, if they did, only kept the recordings briefly.
The only chance is that some third part such as a radio fan might have done an aircheck. But it is also unlikely that they saved a whole day, as even with cassettes, it would take a lot of money to keep entire days, weeks, months. And lots of storage.
And in Spring 1991 (the book prior to your desired period, KLIF and KRLD were not the top stations... KSCS, KVIL, WBAP, KPLX, KQXQ, KKDA, KJMZ and KEGL all beat KRLD and KLIF was not even in the top 10 by then. While the ones you mention had news, they were not the highest billers and likely did not spend much on archiving progamming.