Fraternal (not identical) twins, born aboard a ship traveling west to east across the Pacific. One of them officially born January 1st, 2016. The younger-by-30-minutes twin officially born December 31st, 2015. They'll have the hardest time persuading people that they're really twins once they're grown up.

This works even without timezones. If they're born even a second apart, it can so happen on different days (if they're born around midnight)