Upvote:2
It may have been "Your Story Hour," a small organization based in Medina, Ohio. They aired their stories on radio and produced record albums, some of which are sold as vintage collectors' items on eBay today. If buying their stories today, of course, one can purchase them on CDs.
Here is a link to their website:
https://www.yourstoryhour.org/
The "Bible Comes Alive" albums cover the Old Testament Stories. In their description, one may notice that they were produced by "Uncle Dan" and "Aunt Sue." "Aunt Sue" passed away years ago, and was replaced by "Aunt Carol," so these are legacy stories.
If these stories are not the ones you were remembering, you might consider them as a possible replacement for what you are unable to find. Another possible replacement would be with stories from "Bible in Living Sound." They are newer, and probably were never recorded on vinyl records, but they are also lively audio stories based on the stories of the Old and New Testaments.