If you are not in a position to ask the other party to consider mediation, talk to your attorney and ask your attorney to suggest mediation to the other side.
If you are not represented but the other party is, you could call that attorney and suggest mediation as a way to resolve the matter.
If you are not represented, whether the other party is represented or not, you could contact the mediator you would like to hire and ask the mediator to make contact with the other party to discuss mediation and find out if the other party will try it.
Or you can give the potential mediator's contact information to the other party and ask them to call the mediator themselves to find out about the process.
Here are some guideline questions you might use if you are suggesting mediation to the other party or the other party's attorney, whether you have a mediator in mind or not:
- I know we have been going back and forth over what to do with our dispute for a long time now, so I wanted to see if you have considered having a mediator help resolve our case.
- It seems like we're both spending an awful lot of money to fight this thing out in court, would you be interested in looking into mediation as an option to get this case settled?
-I've read that mediation can save a lot of time and money for all kinds of disputes and we'd still get to make our own decisions. Why don't we try that?
-I don't think either of us likes the potential outcomes if this dispute goes to trial; why don't we find a mediator to work with us and find some more creative solutions for our issues?
- Our legal fights have been very hard on the kids; I heard that mediation is a good way to find agreements that work for everyone, especially when there are children involved. What do you think?
If any of these gets the other party to consider mediation, then you can provide the name of the mediator you have in mind ("I've looked at mediator Jane Doe's website and think she could help us. Do you want to take down her information and research this on your own and get back to me?").
Or you can each do some research, come up with several mediator's names and then either agree on one or toss a coin if you can't agree. Just get started!