Newt, the 12 year old girl introduced in Alien, is killed off screen. Her body has an autopsy performed on it to see if her death was caused by a Xenomorph, but most of it isn't shown, with the camera mainly focused on Ripley's reaction.
There is a dead baby which we never see alive, nor do we see the murder. It is only a ghost baby.
The main character's sister and another teenage girl are killed.
Gone With The Wind
The protagonist's small child is thrown from her pony and breaks her neck.
I Am Legend
There was a helicopter and it went BOOM and the kid in the helicopter was like AAAHHHHH and Will Smith was like NNNNOOOOOO.
A man's teenage son is stabbed in the gut and dies.
Meet the Spartans
The Shrek baby is kicked off a cliff. Britney Spears (a lookalike), carrying her baby, is kicked into the "Pit of Death", a bottomless black hole, which is then flushed like a toilet. We however see both of them alive in the movie's final scene, where the entire cast performs "I Will Survive", among other characters, some of who have died in more graphic ways. It's hard to say if this scene is canon. A child is brutally beaten up by his father for "training", but survives.
Noroi: The Curse
Kana Yano dies. Junko Ishii's neighbor and her daughter die in a car accident.
Rogue One: A Star Wars Story
It is not shown directly, but a child is saved from the middle of a guerrilla war zone in Jedha City, only for the entire city to be destroyed shortly after by the Death Star.
South Park: Bigger Longer & Uncut
Suffers severe burns when he attempts to light his fart on fire, but is ultimately killed by the ER doctors who replace his heart with a baked potato, which explodes and splatters some of his remains across the hospital room.
The beginning of the movie the vampire kills a family and a baby.
A character in a car takes a "shortcut" through a playground. One kid is seen stuck on the front of the car, it may be unconscious or dead, it doesn't move however.
The Girl With All the Gifts
One kid beats another kid to death with a baseball bat. In fairness, the second kid wanted to eat the first kid's mom.
The Starving Games
A little girl is kicked against a tree and dies from the impact. We see her dead body with worms in her mouth.
The Witch (2016)
Almost everyone in the movie dies, including a baby and two small, yet obnoxious, children.
Edward juggles with a baby, an apple and a bowling ball, before letting all of the items fall into his bag. The baby lands in there before the bowling ball, possibly crushing it. We see a character's disgusted reaction, but we can't tell if it survives or not, since it is never seen or talked about again.