The most common are доченька/ сыночек but parents like to use these as well:
December 11, 2016
малыш(m)/малышка(f) - stylistically neutral words
доченька - only for your daughter
сыночек - only for your son
There are also many words that initially have another meanings but can be used like terms of endearment for children. Usually they mean something little, cute or pleasant. They all are informal and metaphorical.
пуговка (small button),
зайка (little bunny),
солнышко (it refers to "sun" but means something like"sweet pie"),
My fiend calls her 4 y.o. daughter "ласточка"(literally it means "swallow" but can be translated like "babycakes").
Here are more tender words for kids: https://www.babyblog.ru/community/post/babyenglish/1726424