I think binance coin has the features you are looking for.it does not fall easily.As the binance develops, its price increases.
BNB is very volatile too. Look to their charts.
https://coinmarketcap.com/currencies/binance-coin/Stable coins and those altcoins that has low liquidity have the lesser volatility. But for those low liquidity altcoins, pump and dump can start. It's not even safe because you will never know when dumping will start.