First, write and ask for convenient dates. Make a record. If you don’t get any convenient dates, or they don’t respond to you, then the answer depends on 1 question: Are you trying to take the deposition of a party to the lawsuit or a witness?
If you want to depose a party, just notice the deposition for a convenient date/time/place. If they don’t like it, too bad. Let them get a protective order if they can. If they don’t show up, run (don’t walk) to the Court and demand an Order compelling testimony plus costs.
If you want to depose a witness, send a subpoena along with the usual notice for the deposition. If you know the witness will not show up (or if the witness will assert some sort of privilege) document it and then Run to the Court for an Order compelling testimony.
In both cases, make the written record and give it to the judge along with your Motion.