I have talked to many Ward Family History Consultants who express frustration because there is no place in their particular building for a family history center or even a dedicated classroom. In the United States, many, if not almost all, of the Ward and Stake buildings now have a functional WiFi network for members to use. If your Ward does not have a WiFi network, it is time to talk to your Stake Clerk and find out why. If there is such a system, you can hold a Family History gathering for teaching and support almost anywhere in the building. If you are persistent enough, you can even set up folding chair for laptop use in the Foyer area. If the Ward or Stake leaders are using the excuse that there is no room to host such a gathering, I suggest using any available space such as a corner or part of the Cultural Hall.
One key to holding such a gathering (I hesitate to call it a class because that implies lessons or lectures rather that research assistance) is using laptop computers. With the Ward's WiFi connection, you can have an "instant Family History Center" in almost any available space.
One challenge is the number of users allocated by the local WiFi network. If a lot of people take advantage of the service, it may "max out" the number of connections. In these cases, there are two options, increase the number of "nodes" available or educate the members of the Ward to turn off their electronic devices during the Sunday School Class time. Most people with scriptures or lesson manuals on their tablets or smartphones can download those files and use them even without a connection. If you are given the excuse that the Ward Clerks need the connection during that time, you might point out that they should be attending Sunday School classes and not working in the clerks' office during meetings.
If the Ward leaders feel that people should be "attending the regularly scheduled classes during Sunday School time." Then certainly follow that council. But point out that the Family History class should be part of that schedule and if you use that time to do genealogy and give support, that is the function of the class in any event. If allowing the activity to take place becomes the issue, then why not schedule the activity either before or immediately following the Block, just like a choir practice or other meeting.
The key here is persistence. The core idea is to provide mentoring and support to members of the Ward needing help with their genealogy. Borrowing a theme from the movie "Field of Dreams," if you hold it they will come. If the Family History Consultants make themselves available at a regular time and place during, before or after the meeting schedule, people will start to come and names will be submitted to the Temple for ordinance work.