As you said, there are no credits -- they're anonymous studio musicians.
But, the "Columbo" rendition of "I'm So Lonesome I Could Cry" is a near-perfect clone of the recording done by The Cowboy Junkies. So, if you get the CJs' version, I think you'll be pleased.
This is in the FAQ, by the way -- just to let you know it's a very popular "Columbo" musical moment.
Sorry I missed the FAQ. Found the CJ's version. Definitely different melody line and instrumental arrangement. Very interesting issue. Apparently some studio musician could have done well w/ a single. Thanks for the info.