I got a CLI from GEMB on my Home Design card, a couple weeks after opening (actually, just a few days after I got the card in the mail and saw what the limit was). $8100 to $9600.
That said, it was something of an odd case. I got the card for the sole purpose of getting 36 months no interest "financing" on a computerized embroidery machine. The machine and software pretty much maxed out the $8100 limit- as in 99.something% util! I called GEMB and asked if they could give me a CLI, since having a maxed-out card looks horrible on the credit report. No problem, she seemed to understand exactly what I was asking for.
Are you showing a lot of use on the cards- i.e., run it up, PIF, rinse & repeat? I'd imagine that would help (though there's no sense in buying stuff you don't need just to try to get a CLI). That's worked for me recently with getting a CLI on my Discover- I use it for pretty much everything (the 5% cash back on gas currently is particularly nice), and I told the guy that even though I PIF, it looks bad on the credit report because I'm using a good chunk of my limit before I PIF.
-MsMS