The station was probably KELP, 920, which garnered a 73% share of the audience. Its program director, Chuck Blore, went on to Los Angeles to establish the landmark station KFWB Color Radio 98 and still is active in broadcasting.
You might check out the jocks listed from KELP on 440satisfaction and see if any of them were there in the 50s. Blore has also published a book about his career. You might also google for his website and email your question.
Here's a link:
http://www.440int.com/440sat.html
EDIT: Another thought - if none of the above works the El Paso Public Library probably has a reference service. Contact them. Shouldn't be hard to look through the papers for stories.

Thanks. Do you -- or does anyone else -- know what share of the market KTRM in Beaumont had in 1957?