They have no genitalia at all, they can conceive from kissing, there saliva acts as sperm. Males and females can lay eggs from this. Often both lay an egg from the same kiss and these are considered siblings. The gender is decided by the gender of the egg layer.

Centaur salivia when inserted in a functional human vagina can rarely produce a weird human-centaur hybrid but those babies cannot survive past a few weeks.

I am just making this up as i go but Its literally impossible to proof me wrong so…