Internationally DL will only upgrade Y/B/M fare classes.
There aren't any copays but as stated above in some cases the upgradeable fares are limited to fewer buckets than other airlines.
You can check upgrade bucket availability on expertflyer.com.
Does DL still not allow same day international upgrades? Unless they have recently changed, their policy is that your upgrade has to clear in advance. If there are still BE seats available on day of flight, they will fly empty (or be filled with non-revs) rather than go to elites with a valid upgrade instrument.