No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
From the two accounts I've gotten, Chase did not take two months to report like Amex. They posted the first time around. My statements were cut 3 days after my due date; the balance on them from statement cut date were reported to bureaus 3 days later.
If you're not applying for any new credit products, just learn to not be OCD about any score drops that occur for just 5-10 days before bouncing back up.
I recently screwed up and PIF'd all my cards and my scores dropped as much as 20 points. But I expect they'll be right back in under a week from today, so I am ignoring the credit alerts if it's just over that one issue. I'm not applying for any new credit products for at least 6 months, so it doesn't matter if my score drops for a week or two.
Being impatient is something to learn to overcome when you're rebuilding. This is a marathon, remember.
Since January 1st, I opened a CSP and Slate. Like Tigers09 said, they're quick to report on the first statement. Chase also sometimes does mid-statement reporting when you pay a card down to $0, so unless it's your daily driver and constantly has a balance you may accidentally get yourself dinged for 0% utilization.