To request an authorized family history center, stake leaders complete the appropriate section of the Request to Create or Relocate a Family History Center form and follow the submission instructions. The stake president and facilities manager sign the form and then submit it to the area temple and family history consultant or area manager.
Authorized centers receive a Church unit number separate from the stake unit number as well as a certificate of license to post in the facility. The Family History Department funds and specifies the type and quantity of furnishings and equipment for the center.
Work with local priesthood leaders to determine a convenient location for the center. It should be easy for both Church and community members to access. The Physical Facilities Department and the Family History Department must approve the placement of the center.
@Name John P Marshall
Providing you are a Member of the Church ...
You might like to consult the the "Helper Resources" in 'FamilySearch'; and, take a look at the "Family History Center Operations Guide"; particularly, Section: 5, "Request a Centre", Page 19. The "Guide" is dated; and, in the process of being up-dated; but, very still gives you the idea/process.
As an aside ...
I am "Tagging" this general 'Question' of yours in this "Community.FamilySearch" Forum, to two (x2) specific 'Groups' in the Forum being:
(1) "Family History Centre Consultants"; and,
...... [ Depending on where, your Ward or Branch, of the Church, is located ... ]
(2) "FHC Technical Support (North America)",
in the hope that, the members of those groups may be able to answer/assist you.
Both, those 'Groups' are "Private"; but, hopefully, you should bet some advise/direction.
@Family History Center Consultants
@FHC Technical Support (North America)
can you give a little "background" as to your question - so we can make sure we give you the best answer to your question.
It's my understanding the they are authorized under the permission of FamilySearch and through the stake presidency.
Family History centers are run by The Church of Jesus Christ of Latter-day Saints. They are generally located in their buildings and staffed by volunteers. And there is usually only one per region because it is limited by space and interest. I am a volunteer librarian and before the shut down we had been cutting back days and hours because of a lack of volunteers (who do not have to be members of the church).
Easier to do is to get your library to become an affiliate of the Family History Library. https://www.familysearch.org/blog/en/familysearch-affiliate-library-how-to/