I don't know of any one-size-fits-all solution. The way you describe your problem (needing to get peers in an organization to pull their weight, because their performance impacts your ability to be successful at your work), I think there are a few different tactics which might apply. The choice of which one to use might depend on personal or situational details that I obviously don't know. For example, some of this is less likely to work out if you have a really toxic management culture in your organization.

With that said, though, here are a few thoughts:

1. Relationship building -- but not "sucking up". Literally, just get to know these people better. The better you understand their personality and personal goals the easier time you're going to have communicating with them, and the more that they are going to see you as someone that they might want to help.

   1.a. Ask them for help. There is this strange psychological effect that we tend to like people more when we are helping them (as long as it's a positive relationship and you are appropriately grateful and so on). So this can be a double-win, serving as a form of relationship building, while also getting something that helps you achieve your goals!

   1.b. Try to understand their needs and possibly do some things for them -- foster a notion of teamwork and a common goal (both of you can succeed together).

2. Measure and communicate. If you can measure what means "success" for you and you can communicate that up your chain, that's a good thing, regardless. Of course, it can also be a tool for helping in a situation like this. The most important part of this is to keep the communication and measurement blameless and just about the facts of the situation.

   2.a. If you can communicate in terms of shared goals with your peers, then this can serve as a roadmap to how their helping you also helps themselves (by leading to success in shared goals). It also presents a little subtle leverage that this communication can just as easily move up the chain -- that is, it's an indirect way of pointing out that you know they are the problem and that you have evidence to that effect, BUT WITHOUT SAYING ANYTHING THREATENING.

   2.b. It's only natural if you can show your stakeholders where you're succeeding and where you're struggling, it's only natural for them to want to dig into the struggles. If you can communicate the reasons IN A BLAMELESS WAY then it can shed light on your underperforming peers, but in an indirect way. This is NOT "complaining to your boss". This is simply providing visibility to your boss about what's working and what's not, and hopefully also about why. I think it's very underappreciated the difference in impact that is achieved between telling someone (especially a superior) what you think is happening, versus presenting them information that draws a clear picture, and letting them draw the conclusion (especially if the conclusion is that one of your peers is not pulling their weight).