Good question. It's not exactly an AMM, but a new decentralized order-book exchange was just announced: Haveno, a fork of Bisq which was based on BTC and mostly used for exchanging BTC-XMR. Using XMR as the base currency will make it faster, cheaper and more private.

An AMM would probably require a sidechain to run smart contracts on, similar to Tari for NFTs, but privacy in itself is not an obstacle. Secret Network is close to what you're looking for.