It depends on the places, where the cat leaves its droppings.
Usually cats prefer places with soft and loose soil like freshly raked flowerbeds or sand.
If that's the case you can place chicken wire over the ground.
At least my cats dislike that.
An alternative is a layer of rough bark mulch.
This also prevents cats from digging holes and burrowing their droppings.
In case your neighbours' cats don't dig but place their droppings on flat ground and possibly everywhere e.g. on the green, you have to resort to other means.
There are certain substances that deter cats with their odour, available at hardware stores.
Some of them are based on plant parts which are disliked by cats others are synthetic deterrents.
Deterrents are spread on the floor where cats leave their droppings.
A major drawback is, that most deterrents are washed away by rain and have to be reapplied regularily.
I consider deterrent devices based on ultrasonic sound as inhumane to some degree, so I don't recommend them.
For difficult cases there are automatic robots with an infrared eye and a electrically controlled water hose.
While expensive they seem to be effective.
lifehacks.stackexchange.com/users/2737/Ariser - reinstate Monica
I once read that cats will walk around used coffee grounds.
Just place some piles in the places where the cat goes and it should avoid those areas.
Ofcourse you will need a lot of coffee to protect your entire garden, but it might be a start to protect some areas.
PS
: I'm told this will also keep away snails.
lifehacks.stackexchange.com/users/9772/Nils Tiebos
Liking cats I know that they like it safe and secure, donot like surprises and generally hate water.
You need to wait until you see the cat coming into your garden.
When it prepares itself to defecate, you take this : which you filled with ice-cold water and... surprise .
The range of the soaker should make it possible that the cat is notprepared .Hit
it one or two times and the cat won't bother to visit you everagain.
You should be aware that you should not do that if youactually like the cat, it will not forgive you.
lifehacks.stackexchange.com/users/4476/Thorsten S.
A good thing I tried was planting catnip, because they like to lie on it, and so keep it clean.
It makes a flat carpet, especially after they've been lying on it.
lifehacks.stackexchange.com/users/2569/RedSonja
I never tried this.
Found this question on quora, https://www.quora.com/Does-blue-colored-water-keep-dogs-away .
Some people say blue colored water help to keep away the dogs.
As per the answer, it does not guarantee it.
But it is worth a try with those neighbor cats.
Take a bottle and fill some colored water and keep it in you garden.
Another idea, just keep some air filled balloons in the garden.
When cats try to play, balloon explosion happens and cats will run away.
Try this for a few days and eventually they will change the place.
Please let us know the result of these experiments.
lifehacks.stackexchange.com/users/4409/MoonMind
My mum had this problem, the cat would pop over the fence from the neighbour at certain places as they're too lazy to walk all the way round the fence - so she ran some old CDs on a string over the ground where the cat would jump down.
Stopped the cat from jumping down, so no cat in garden.
but otherwise, until someone invents a robotic water-cannon guard bot (oh I'd crowd-fund one of those!)
buy a dog?
lifehacks.stackexchange.com/users/9788/gbjbaanb
Here's a method i've heard of, but have not yet used, as we haven't been so desperate.
Mark your territory.
Spread pee from an adult male around the perimeter of your property.
Animals will smell it and won't dare to enter.
However, people might smell it also...
You'll have to refresh it every so often.
lifehacks.stackexchange.com/users/141/Scimonster
One of my neighbours cats keeps using my garden as a litter box. This is quite unhygienic, especially for children.

I've tried shooing the cat away every time I see it, but this strategy clearly isn't working. How can I humanely persuade the cat to either not defecate in my garden or to not enter it altogether?

Given that I think the cat is mostly there during the small hours of the morning the solution needs to not required human intervention.
Humanely persuade neighbourhood cat not to defecate in my garden
lifehacks.stackexchange.com
<gardening><pets>
lifehacks.stackexchange.com/questions/8106
lifehacks.stackexchange.com/users/8157/Flexo
To persuade a cat not to defecate in your garden, you could try covering the ground with chicken wire or bark mulch. There are also certain substances you can buy that deter cats with their odour, or you could try coffee grounds. Planting cat nip might deter them from defecating there because they like to keep it clean. More extreme solutions would be to spray the cat with cold water when you catch it or to just buy a dog. The options are to place chicken wire, rough bark mulch, coffee grounds, balloons, coloured water or a string of CDs in the garden, to install an automatic hosing device, to douse the cat with cold water or plant catnip to sprinkle adult male human urine around the garden or get a dog.
Place chicken wire over the ground or rough bark mulch and if that fails try deterrents, including automatic hosing devices. Put used coffee grounds in the areas frequented by the cats. Douse the cat with cold water just as it is about to defecate. Plant some catnip. Place a bottle filled with coloured in your garden or keep air filled balloons which will burst when the cat claws them and frighten it away. Hang some CDs from a string and it will frighten the cat away. Or get a dog. Spread urine from an adult male around the garden.