Frombaby +‎-kin.

babykin (pluralbabykins)

1. (endearing)youngbaby.
   • 1922, Florence Ashley Beeler, “Perfection”, inThe Kindergarten-primary Magazine, volumes35-36, page112:

     There is nothing so sweet, or so quaintly complete As a dear littlebabykin's queer little feet, With their ten tiny toes like the buds of a rose And their heels soft as velvet.

   • 1934,Dramas - Volumes 17-18, page210:

     Italia was two years and two months old, And Tony was ababykin two months old.

   • 2002, David Grossman,See Under: LOVE,→ISBN:

     But thebabykin wouldn't stop screaming, and if you've ever heard Fried sing, you'll know why.