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

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.

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.

Nonchalantly execute the ducks in front of the kids. You'll also be supporting your local youth therapists job security.

Put up a sign that says, "Pursuant to ordinance 347-1236, a sexual predator resides here"

CAUTION:
BIRD FLU

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.

Build an exact replica of that area right next to the original. They'll be confused, are they visiting the real ducks or a simulacrum of the ducks?

Warning: Kids left unattended on this lawn will be fed to dinosaurs in the name of science.

Parents and dogs will be given popcorn and adequate seating.

My joke answer is to directly tell them that they are not allowed to come on your lawn, to not let their kids do the same, and that it's your property, not a zoo.

This way you'll guarantee that your house is egged often enough that some of the eggs may not break, and some subset of those could be adopted by the ducks and hatched into baby birds that the kids also won't be able to come look at.

Make sure the place they stand has no vegetation, and is always soaked, so their shoes inevitably get muddy. When they track the mud inside their houses, their parents will flip out and tell them not to go to your property again.

Or just put a motion sensor sprinkler to spray them when they get close.

Build a moat. It would certainly keep me out.

A sign: "Ducks carry Avian flu, please keep 500 Meters away to avoid transmission risks"

Put up a sign that says “WARNING: rabid ducks, enter property at own risk”

Start handing out kazoos.

Can I non-jokingly ask why that's such a big deal? If it's all up in your grill I get it, or some stupid liability thing. Otherwise, there's little enough joy in the world, what's the harm?

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.

Handwrite the URL of this post and put it through their letterbox

Satanic iconography

Update your landscaping to modern fire-swamp and stock it with many rodents of unusual size.

Decorate your home like a child's bedroom.

Have photos of only you everywhere, esp in the bathroom and hallways.

Invite just the parents over for dinner. Serve blue rare steaks and have the fanciest silverware arranged on the tables.

Cover your yard in red paint, chunks of meat and feathers? You wanted humour, but was that a bit too grim? Sorry…

Put up a gate and a sign saying “$1 Entrance Fee”. If you want to get even sillier, draw a horizontal line about 7ft off the ground on the sign plus the text “Must be at least this tall to enter”.

Charge admission.

train the ducks to chase after the enemies. Lol

Trespassers will be trebucheted.

"There is at least one more bear trap on my grounds than you can spot."

I would have to go with landmines. If that isn't enough of a deterrent, and claymores or even some bouncing betties.

Ask them if they want to get battletoads instead

HIMARS

Play the sound of a loading shotgun through a speaker when they trespass

"Entry Fee (min one):

• Carrot
• Apple
• ..."

That way you get duck (or human) food for free.

Walls, barbed wire, around the entire perimeter. Hire a pmc to patrol the grounds. If the kids are caught, extraordinary rendition them to a blacksite in an allied former Soviet state. If they escape before capture, send out operatives disguised as soccer/little league/gymnastics coaches until you locate and black bag them. Same fate as the initially captured. They’ll either get the memo or run out of kids

Give the ducks a nice shower/sprinkler set up that's both timer and manually controlled.

"I'm assisting as part of an experimental penal system. I just want you to be aware that all of these ducks were once human child rapists who were transformed in exchange for lighter sentences."

Get a shotgun, load it noisely when the kids trespass

Tell your neighborhood you're a sex offender?

You could make sure they see you taking a dump on the closet edge of your yard, build a fence like that and I think they'll get the message