Dennis,
My wife is from Saint Matthews in Louisville and so I am a little familar with karaoke in Louisville. Your best bet, however, is to grab some of the free newsweeklies and check out the entertainment sections since karaoke shows seem to come and go at different venues. There are at least two popular newsweeklies that have entertainment listings. I think one is called "LEO" and another called "Velocity". They give these newsweeklies away all over the place like at gas stations, grocery stores, coffee shops, etc... In addition, I'd strongly recommend calling the venue before going there to verify that they are actually having karaoke that night.
Oh, here you go, I found some useful links for you... Remember to call first!
http://www.velocityweekly.com/apps/pbcs.dll/article?AID=2008802270933
http://www.leoweekly.com/karaoke
Sorry I can't be more specific, but as I said the shows seem to come and go... That being said, you might want to check out Creekers. Let me know if you like it there... I've only been there once and I thought it was ok!
http://www.creekersbarandgrill.com/
I used to like Phoenix Hill, but it's been years since I've been there. You may want to check it out, however, pretty cool place...
http://www.phoenixhill.com
--Tad