Trying to Re-Download an app

So basically I used to have this iPod Touch and I purchased a few apps on an account I no longer use anymore. I want to Re-Download these apps on my iPhone but every time I sign in it says "There is a billing problem with a previous purchase." and directs me to a page wanting me to add a new card, but you see I just got a new card so it has zero balance and won’t go through. So I’m wondering if there’s any way to Re-Download them without adding a card because the "none" option isn't even showing up.

Any help would be greatly appreciated.