Prepare. If you do your homework beforehand, you'll know when you get past the point a deal is worth it for you. (This is called a BATNA...google it to learn more). You can be confident going into a negotiation that you have a very strict walking away price and won't let your need to find harmony put you in a worse situation than where you started.
Team up. Bring someone into the negotiation that likes a little bit of conflict. It will balance you out and keep you in check if you're settling too quickly.
Avoid in-person meetings. If you tend to cave when you're in person, send a proxy, do it over the phone or maybe even email. It's really easy to hold your ground when you're not there in person. It's harder to read social cues through those mediums, but it might be worth it for a people pleaser.
Be optimistic. For a lot of people pleasers, this just makes you more comfortable. In tough situations, remind whoever you are negotiating with that you are still optimistic you'll be able to reach a deal.
Take a timeout. It's like a timeout in basketball, if you feel the heat from the other side and it makes you want to settle, just kill the momentum by taking a break. If you're on the spot, say you need a class of water or need to go to the bathroom.
Negotiating well is a skill. Even if it does not come naturally, with effort and a little bit of practice, you can greatly improve your skills. If you want to learn more, I recommend "The Truth About Negotiations" by Leigh Thompson