KANSAS CITY, Mo. — Sha’Quille Kornegay, 2 years old, was buried in a pink coffin, her favorite doll by her side and a tiara strategically placed to hide the self-inflicted gunshot wound to her forehead.

She had been napping in bed with her father, Courtenay Block, late last month when she discovered the 9-millimeter handgun he often kept under his pillow in his Kansas City, Mo., home. It was equipped with a laser sight that lit up like the red lights on her cousins’ sneakers. Mr. Block told the police he woke to see Sha’Quille by his bed, bleeding and crying, the gun at her feet. A bullet had pierced her skull.

In a country with more than 30,000 annual gun deaths, the smallest fingers on the trigger belong to children like Sha’Quille.

During a single week in April, four toddlers — Holston, Kiyan, Za’veon and Sha’Quille — shot and killed themselves, and a mother driving through Milwaukee was killed after her 2-year-old apparently picked up a gun that had slid out from under the driver’s seat. It was a brutal stretch, even by the standards of researchers who track these shootings.

These are shooters who need help tying their shoelaces, too young sometimes to even say the word “gun,” killed by their own curiosity.

They accidentally fire a parent’s pistol while playing cops and robbers, while riding in a shopping cart, after finding it in the pocket of the coat their father forgot to wear to work. The gun that killed Sha’Quille last Thursday was pointing up, as if being inspected, when it fired.

Image Sha’Quille Kornegay shot herself with a 9-millimeter handgun she found while staying at her father’s house. Credit... Haven Parrish, Jr.

They are the most maddening gun deaths in America. Last year, at least 30 people were killed in accidental shootings in which the shooter was 5 or younger, according to Everytown For Gun Safety, a gun control advocacy group that tracks these shootings, largely through news reports.

With shootings by preschoolers happening at a pace of about two per week, some of the victims were the youngsters’ parents or siblings, but in many cases the children ended up taking their own lives.

“You can’t call this a tragic accident,” said Jean Peters Baker, the prosecutor of Jackson County, Mo., who is overseeing the criminal case in Sha’Quille’s death. Her office charged Mr. Block, 24, with second-degree murder and child endangerment. “These are really preventable, and we’re not willing to prevent them.”

Gun control advocates say these deaths illustrate lethal gaps in gun safety laws. Some states require locked storage of guns or trigger locks to be sold with handguns. Others leave safety decisions largely to gun owners.

Twenty-seven states have laws that hold adults responsible for letting children have unsupervised access to guns, according to the Law Center to Prevent Gun Violence, though experts say such measures have, at best, a small effect on reducing gun deaths. Massachusetts is the only state that requires gun owners to store their guns in a locked place, though it has not stopped youngsters there from accidentally killing themselves or other children.

Gun rights groups have long opposed these kinds of laws. They argue that trigger locks can fail, that mandatory storage can put a gun out of reach in an emergency, and that such measures infringe on Second Amendment rights.