Chilren of a friend of mine referred to their genitals as 'my linky' which makes some kind of sense...
My DDs learned the proper words (though yes, admittedly it should have been 'vulva' and not 'vagina' - ) but that did lead to some embarrassing situations ....DD1, in the queue in Boots: 'MUMMY! My vagina itches!' and DD2 announcing on a bus journey that the rumbling bus engine made hers tickle.
One friend refers to 'down there'; my daughter's surgeon, a Lt-Col in the army, referred to 'your undercarriage' and I use 'fanny', 'miffy', 'lady garden' or whichever term I find most amusing in the circumstances!