Are you positive it is because the collection is 'unpaid' ?
You would have to apply again unless the CC would do a soft pull when you can recon. If you can recon i.e. Was it a BOA secured? I think Orchard secured is pretty easy to get. I got it with 4 unpaid baddies. CUs are very good too.
Here is the story I'll try to keep it short.
So I was applying for a Worldpoints card with Bofa but was denied they counter-offered with the Platinum Plus Visa card with a $500 limit. So I took their offer. A couple months later I sent a message to a representative asking when they usually give increases their response was my account was never eligible for an increase and I would never be able to do a product change.After investigating I found out that it was not a unsecured card but a secured card that I didnt have to put any money into the account. I called and they told me that the best thing to do was to open another secured card because I was eligible and that that would help me in the future. Hearing how well secured cards work and how they helped people I applied and was denied because of the collection that never updated.
I have tried Capital One and their service stinks. I had to fight to get lates off my credit report because I was hospitilzed and they didnt want to pay even though I paid the payment protector.