This is surprisingly difficult. The Hopeful Gospel Quartet have recorded an album called "Climbing Up on the Rough Side," which contains the song of that name. You can find information about the album at HighBridge Audio, and at many other sites, but I haven't found any that have sound samples.

If a song has been performed on PHC, normally you can go to A Prairie Home Companion's website and type the song title into the search box, and it will tell you exactly when the song was performed. Then you can listen to the archived program. But searching for "Climbing Up on the Rough Side" comes up with only references to the album.

I found a brief quote here: http://www.chicagotemple.org/Carillon/2004_03_26_Carillon.pdf

"I'm climbing up on the rough side of the mountain,
I gotta hold to God's hand (his powerful hand) (God's unchanging hand).
I'm climbing up on the rough side of the mountain;
I'm doing my best to make it in."