Conflict resolution is really hard to max out. When the child is in the toddler or child stage, parents can teach them to say sorry. At first, they won't want to listen, but soon, they'll always listen. After that, have parent encourage learning to say sorry.
Other way is to find random sims, get them to fight somebody and then have your child or teen try to fix the bad relationship (Friendly). Even if it doesn't succeed, it will build that character value.
Mediator trait comes useful when you want sims to stop fighting. These sims always succeed in fixing the bad relationships. These sims are also easier to talk to when sim have bad relationship with them.