How do you kill children?

Console commands are too much effort.

Fortunately for us, there's a mod. The Killable Children mod:

Allows the children of Skyrim to die. Affects the Breton, Imperial, Nord and Redguard children.

You can download it from Nexus Mods here. (Note that Nexus Mods requires you to sign up for a free account for age verification purposes, I believe.)

Open the console (` by default).
Type in help <kidsNameGoesHere> 4. You'll see a list of ID's, one of them will say something like:
_NPC (somenumberswillbehere) kid'sname
Next type in SetEssential <thenumbersfrombefore> 0 at the console and hit ↲ Enter.
Replace with the kid's npcID, and he should be killable, unless Bethesda implemented their invulnerability in a unique way.

The mods, Killable children V2 and Killable and Lootable Children allow killing of children, but at the same time, setting as unkillable or 'essential', certain quest-related children, preventing bugs and avoiding missing some quests, which is like the vanilla Skyrim behavior where certain quest-related NPCs can not be killed.

The Killable and Lootable Children mod also allows you to loot children, and makes the 'essential' children, 'non-essential' when their related quests are finished.