That sounds like the rifle a friend of my grandparents (we called her "Aunt Mary" as an honorific) had when I was a kid. She let me and my brother shoot it in her apple orchard. I was too young to know much besides how to sight it and pull the trigger but based on what I can remember 60 years later, I'd say it was a falling block single shot.It is a single shot, curled lever action.
Just FWIW, that is not a "child"s rifle", it is a full-sized single-shot 22 rifle. "Boys' rifles" like the (Winchester 1902, Remington Rolling Block Model 6, Savage Model 3, or the Stevens Little Scout shown in Drm50's attachment) were designed specifically for younger shooters, and so had shorter stocks and barrels, and were more economically priced and of lower quality construction.I have a single shot .22 child's rifle