We spent a month riding slowly around Ethiopia (southbound) with no rock-throwing problems. We received good advice beforehand, as follows below, from an experienced northbound British couple, in Sudan, who also had no problems (driving a Landrover).

Except in the cities, private vehicles are virtually unknown. On the roads outside cities there are only buses and trucks, and very few of them.
So the roads are literally full of pedestrians and animals going about their business. And they have right of way. Adults carrying water and ploughs, and herding animals, children playing, huge groups of schoolchildren going to classes.

And they want the freedom to wander around the road without having to worry about strange traffic hitting them.
That includes, for instance, adults carrying huge wooden ploughs on their shoulders who cannot see behind but suddenly want to cross the road. In doing so their plough swings round across the road and they don't want some vehicle crashing into it.
That's reinforced in their mind by the fact that if a vehicle hits a pedestrian, in any circumstances, the rules say it's the driver's fault.

So you have to go slowly.

As it was, we were on small 250cc bikes, so rarely reached 80kph on the few empty stretches of road. Wherever there's a significant number of pedestrians you need to be at no more than 60 - 70kph, depending. Even less in villages.
Even at that speed, sometimes on entering a village, adults would give a little hand signal, sort of waving down towards the ground, which means "slow down." These adults have children playing around somewhere in the road or going to classes. Or their animals are on the road.

So, if you travel at a speed that respects all this, what you'll find is that everyone will wave at you. And you just have to wave back, equally as spirited. Or the stone throwing will start.
Or if you're simply going too fast in the first place you'll just get stones thrown at you.
As well as waving, the children will shout "you you you" and run up, hands out.
This is in response to the endless tourists who travel through this country (fewer now I think) and who throw pens, notebooks, money or sweets out of their windows without stopping. We were told that in schools now, children are taught to no longer expect stuff to be thrown out of vehicles, and to not run around begging, but that's probably a slow process.

If you find, because of all the people and animals around, you can't take your hand off the handlebars to wave, you are absolutely going too fast. No question.
Adults will wave as well if your speed is OK, but not come running and begging. But if you don't wave back you'll see an immediate bad look in their faces.

If you find it all gets too much and need to stop, or need to buy stuff, as soon as you come to a halt, get your right glove off quickly. By then dozens of children will have reached you with hands outstretched, begging. Immediately you have to shake all their hands, saying "Hello how are you? No I don't have any money or pens!" with a big smile on your face. They'll immediately forget they were asking for that stuff and want to know all about you instead.
If you engage with them all properly you should find that no one, that you have properly shaken hands with, right down to 18-month-olds, will dare to touch anything on your bike. As well as "you", they'll probably also know the words "where", "who", and "why".

Occasionally (it happened to us a couple of times) a teacher or someone else who can speak English will come up and start translating. You'll be there a half hour at least. Taking lots of photos will be welcomed.
Then when it's time to go you'll have to shake all the little hands again and they'll all wave you off. If you're sitting on your bike, 6-year-olds will lift up 1-year-olds so you can reach their hands.

Ethiopia is a country that you just can't travel fast through, and we had nothing but pleasant times there.
This is the experience we had, and speed of travel was the key.

You may feel, if you do get hit by a stone, that giving chase is the thing to do. Only you can decide.
But you need to remember that stone-throwing is a common skill in Ethiopia. Herdsmen use it to control animals (no dogs are used for this). Mothers use it to control the wanderings of tiny children (not hitting them, but hitting the ground ahead of them). Children aren't often responsible for either of those, so they practice their skills (needed in later life) by controlling the speed of the three or four vehicles per hour that may pass by, if they're going too fast.
So if you catch someone, they'll think it strange that you chase them in response to their legitimate action in trying to slow you down.

We discussed this with various cyclists we met, as they too say the same. Some of them get stones thrown at them, some don't. We came to the conclusion it's still a speed thing. Bicycles are silent, so are expected to travel even more slowly as they can't be heard. And if cyclists don't wave, their speed makes it easier to throw stones at them.

The British couple in Sudan gave us one extra bit of advice if you're on 4 wheels - never have your windows wound up, and whenever you stop, get out straightaway to shake everyone's hands.

So to sum up:
SLOW down and WAVE! And enjoy the welcome.

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TTR250 - London to Cape Town