You get a good credit score by borrowing money and paying it back faithfully, not by being perpetually in debt. I carry a mortgage but no other debt, and pay off every credit card balance before charges or interest accrue, and my credit score is solidly in the top range.
I know it's a crazy concept, but to be considered a safe person to lend money to, you have to actually borrow it sometimes and prove that you will pay it back.