I don't see a problem with `tourism=zoo`. Nothing says that it may only be used for "big" zoos. And I know quite a few really small "zoos" with only 5 or ten animals, they're quite common in public parks.
The fact that it is on private property and non-commercial is irrelevant (most zoos are on private property as well, and small zoos are often free of charge), and the size should be apparent from the map. Ideally, try to add the tag to an area, not just to a node, so people will see that it is small.small.
One caveat:
I would only tag it if it is actually meant to be public. If there are for example signs for it visible from the road, I'd have no problem with it. If it's really only for people the owner knows, or only for people from the village etc., I'd consider not tagging it at all.