Great idea .
I think start with a rabbit . NOT really a farm animal per say but the kids could get into a routine of feeding & cleaning & caring for such a gentle one to start .
Good luck

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chickens are good because they could run around free range and kids love collecting eggs, plus they're quite safe around little ones.

We raised goats and loved it. As children, we helped feed, milk, and care for the goats. We saw baby goats (kids) being born, we played with the goats and we learned a lot about responsibility. Goats can be great for toddlers... as long as common sense is used. [You must be registered and logged in to see this image.]
We usually removed the horns from most of our goats. It was safer for children and adults.
pygmy goats are smaller and might be something you'd be interested in.

I raised a cow from baby up. It was fun and that cow was like a best friend.

A horse or pony is always great... but some don't consider them farm animals.. in the same sense as cows, goats, pigs, sheep and others.

Pigs can be quite the friendly pets. lol Some people even go as far as having pigs as pets in their homes.

I think a lot depends on the disposition and time taken with certain animals. If an animal has a mean disposition... not much will make it great for kids or adults. Time spent with animals and getting them use to people makes a huge difference.

I had a rabbit when I was a child. That was another great pet. I could carry it around, feed it and learned to care for it.