Instead of pushing the person toward agreement, draw them in the direction you want them to go. Build them a bridge across the chasm between you and them. Involve the other side A common consulting mistake is to announce that you have found the solution to a problem. It's much better to get the parties involved to design an agreement together. Ask for and build on their ideas.
Effective consultants do more asking than telling.
The simplest way is to involve other parties is to ask for their ideas. Ask how they would solve the problem, deal with the issue, or make the decision to meet everyone's interests. Once you've obtained their ideas, build upon them. Select the ideas you find most useful and head off in the direction you want to go. You don't have to accept their ideas as they are.