Well, I scoured the internet for a bit again. The best I could find was a youth-sized one. Do you know who the manufacturer is?
Wow, this is the first time I've heard of someone preferring the old L.
http://www.sportslogos.net/logos/view/2842/Louisville_Cardinals/2001/Alternate_Logo
Here is a grey beanie with the old logo that I found on Google Shopping
the child version of the hat you are looking for!
I'd check JD Becker and Campus Wearhouse locations, they don't have a lot of turnover with hats (or anything that doesn't immediately sell really) I once found a jersey at JD Becker that was on sale and something I had stocked when I worked there 10 years prior. (It was a Urrutia #7 iirc)