I have seen examples of having young children use LEGO bricks to build sailing ships (or steam ships), covered wagons, tents, homesteader shanties, etc.
And what young child doesn't enjoy a well-told story from an ancestor's life? That was the first thing that hooked me on family history! (... a family fleeing famine-ravaged Ireland in 1847 on a ship that nearly sinks in a storm, surviving a plague and then establishing themselves in a total wilderness ... Who could resist wanting to know more?)
Drawing and coloring pictures based on a family story is something that can be enjoyed by very young children.
One interesting idea I saw was to have a child color outline maps of countries, states, or provinces that their ancestors came from. RootMapper or Grandma's Pie would make it easy to identify those areas.
One superior blog on this topic is http://www.growinglittleleaves.com That is where I found the map-coloring activity. I quote from the Contact page:
"Welcome! My name is Emily Kowalski Schroeder and I am the creator and author of the Growing Little Leaves blog. After working as a scientist, I made the decision to suspend my career and stay at home with my children on a full-time basis. I soon became an avid genealogical researcher, and began looking for age-appropriate ways in which to engage my young children in learning their family's history. Somewhat dismayed by the lack of family history education options for younger children (toddlers through elementary age), I decided to develop my own genealogy education activities for my children and share them with others via my blog, Growing Little Leaves.
"In July 2014, I entered into a partnership with the Indiana Historical Society. Our goal is to provide quality genealogy educational programming for both young children and their caretakers."
If you want young children to enjoy family history, I suggest you visit Emily's blog.