In my opinion, the most stable altcoin - is the litecoin. Long time this coin have almost constant 1/100 of the bitcoin value.
I guess there is no stable Altcoins because all of them are mostly they are sudden change or they are volatile, so they not stable. But even they are not stable some of them are worth it to have, especially to those Altcoin that have potential and some of them are now valuable. But just be careful of choosing Altcoin because nowadays there's a lot scam altcoin is caming out, its better to trust in altcoin that many people who believe and support to it, like Ethereum.