Kiddie ride
From Tardis Wiki, the free Doctor Who reference
A kiddie ride was a small mechanical ride, often found outside supermarkets, which was designed for children. The rides usually cost around 50p per go, and would gently rock the passenger while in operation.
These rides often had designs that would appeal to children. One outside the Happy Price was designed to look like a horse, while another imitated the popular title character from Thomas the Tank Engine. (PROSE: The Wrong Hands)