No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
In my experience, Capital One goes off a script and their great desire not to grant me a CLI under any circumstances.
Oh wait... I did get a $300 CLI once after a lot of sweet-talking - I take it all back.
Seriously... I think when I've asked for a CLI they've pulled a soft, but I get the impression that what they want to see is a LOT of use of your card at its current limit. Along with, of course, making timely payments and such.