Only way is miles or SWU's. If you haven't taken your Choice Benefits yet then go ahead and pick SWU if you want to. They will deposit in your account immediately and you can use them on your flights. They are valid for any flight as of the time they are deposited in your account.
You should call DL first and ask about the upgrade possibilities on your flight. There's a decent to excellent chance that upgrade seats do not exist this close to your flight. They can tell you how the loads look and whether you stand a decent chance or not.
-RM