“Unattended Children Will be Gifted a Duckling”

You’re looking at this wrong way.
Buy a gumball machine. Put on fence. Fill machine with enough feed for the day. Charge other people to feed your ducks

Get you some geese

Pro tip - feed them a handful of dandelion leaves twice a day, they’ll be your best friends

My grandmom used to hang dead birds in her garden to warn others from coming to eat her berries. Maybe this works with kids too, you just need to get a dead one from somewhere first.

Get some thick over sized glasses that are that transparent brown colour on the rims, grow a thin but dirty moustache, only wear faded pastel tops and short stained shorts that are 1 or 2 sizes to small, ALWAYS show your belly, make sure to be overly friendly but never blink when making eye contact, sooner or later they’ll all leave your house alone.

Raise a pack of cats then put your cat on guard your property.

Their meow will scare kids away

Obvious answer is to give the kids ducklings for every visit. Pressuring kids parents to stop their kids coming over without permission. Unless they want to own duck pets.

depending on where you’re from you can hang up a sign saying “trespassing Children will be converted to Islam”

Had a friend with problem neighbors kids cutting through his yard to get to the store. He was friendly with the parents and didn’t want to stir shit. The neighbors were super all-natural, hippie, no chemical types, so he told them he switched to a new fertilizer packed with micro-plastics and forever chemicals made by Monsanto that he had to sneak in from Mexico because it wasn’t allowed in the US. That fertilizer sure worked because the trail the kids were carving filled right in that summer.