How can I help bullies feel better without having to put someone down?

You can take by force, but you can't give. Statistics show that bullies themselves are likely to have troubled families or turbulent past - so aggression can be a defense reaction. That is not to say that they are beyond help - it just might take time and the type of help that you can't immediately provide to relieve that person. However showing kindness to people and approaching them with understanding (even if that means to keep some distance) is always a good advice! :)

Bullies have dark past and they are the people who struggle the most, you can offer a shoulder to cry on or ask them to vent about their problems because some of their problems that they struggle with is thinking nobody cares about them but if you asked them to vent they would feel a lot better and they would know that someone cares about them

Ask them what's wrong. Talk to them, but listen more. Figure out what they might be struggling with and help guide them through that or provide them resources to do so. Pain is not something that should last forever.

Being nice to bullies can be hard, but bullies are usually very insecure and need compliments just like everyone else. Treating bullies like people (greeting them and talking to them) will help them feel better about themselves, and you don't have to put anyone else down.

Let them know they're better than that and that hurting others isn't helping them and they are a good person without hurting others.

You can compliment them and make them realise their worth. Not only will you being kind to them make them feel guilty, they will also see that they don't need to be so lonely and that they arel iked by other people regardless of whether they make others look bad.

Understanding that bullies have their own problems, whether insecurity or anything else, and actively listening to their own problems would be my technique to help them feel validated without condoning behaviour that hurts others. Actively listening could unearth problems that they may or may not have confronted yet, and allow for deeper healing. In a way, I think that this would help with cutting the problem at its source. Although it is difficult to say that all bullies bully for the same reason, there is no reason why compassion and empathy towards them should do anything but help. To me, it seems like it can't do any harm.