When you find yourself trying to remember a show (or any works) that's on the tip of your tongue but just out of reach, come here - the collective brain of the TVTropes community can probably help. Post all the details you can remember (examples help). If you're looking for a trope, head over to Trope Finder. Have general questions about tropes? Visit Ask The Tropers!
I don't know about multiple tigers, but Tiger by the Tail by Eric Walters definitely has a boy and a girl who meet an eccentric neighbour (who's a former circus performer) who keeps an exotic zoo which includes a Tiger named Buddha. The Tiger escapes and the boy and girl and the neighbour have to find it before the authorities take the man's whole zoo away.

There was a novel which was about a boy and a girl who meet a strange old man who keeps tigers in cages in his basement. The tigers were also in danger of being taken away.
Anyone remember the name of the novel?