I have fond memories of riding a squeaky spring rocking horse like this one at my grandmother's house. She kept it in her toy-filled basement, which was probably a good idea since the toy was so noisy. Either the horse would be being ridden madly, or my brother and I would be loudly fighting over whose turn it was!
We also had a rubber bouncy toy you sit on and hop around the house on - I think it was shaped like a chicken, or maybe a hippo. (The fog of time is making it hard to remember!)
We enjoyed our rocking horse, bouncing toys and rocking chairs so very much, I'm looking for a more unusual, perhaps more whimsical one to keep in my playroom. It may not make sense for you to have a rocking toy in your house - they're fairly inexpensive nowadays, but take up space, and are a one-purpose item. If your niece and nephews don't visit often, or are likely to only be able to enjoy using it a few times before they physically outgrow it, it probably isn't a practical thing to keep around your house. They are also dangerous - you don't want wheeled riding toys if you have stairs or a multi story house; fingers can get pinched; kids can fall off and get hurt, etc. Use with caution and supervision!
If you have the extra room for it though, and have as many small children visiting your house as I do here at mine, here are some cute alternatives to boring standard "rocking horses." I'm tired of horse, farm, zoo and safari animal themes!
And now for the unaffordable whimsical fantasy dreams: