I could only find one reference to a real Klingon lullaby. The Doctor on Star Trek Voyager called it "Sleep Little Warrior." ( You Tube Link ) The problem is the Doctor never sings the actual song. But, don't worry I did find a great website that lists a bunch of songs in Klingon. They even have the lyrics for a few children's songs. Below is a sampling of what they offer:
Row, row, row your boat or I should say ro' ro' ylbot
toghmeH bom a counting song for the number 0 to 9
There Was an Old Lady Who Swollowed a Fly or yIH ghupbogh be' qan
I don't speak Klingon so I can't verify the accuracy of their translations, but these people seem like pretty serious scholars so I am just going to trust them.
You Tube Link
Oh, and I am pretty sure this little one already knows lots of Klingon lullabys.