"That boy is marrying my young cousin."
Translation:Tamhleten chlapec si bere moji mladou sestřenici.
"Ten chlapec si bere mého mladého bratrance" is accepted. Your sentence is questionable because "žení" really means "takes as a wife (as his woman)" - it's tough to decide whether it's correct or not. But native speakers do use it (for gay couples), since the gender-neutral "brát si" doesn't always come to mind quickly enough.