I suspect the table at least has to have the same name. Could you try to rename the tables so the new one is info_2010 and see if it works?
I'm not sure if MySQL allows to edit data in views, but if yes, a solution could be to create a view, e.g. ‘current info’:
CREATE VIEW current_info AS SELECT * from info_2010;
and then change it each year to point to a different table.
Thanks for the suggestion, I tried, but the problem I am having all seems to be at the Filemaker end. I go to Manage Database and click the Relationships tab. From here I can add the other table (info_2011), then I select the layout and then choose Layout Setup, Show Records From info_2011. When I click OK, the fields in the table show <Unrelated Table>. If I delete info_2010 from the Tables, and rename info_2011 to info_2010 the message is then <Table Missing>. I could manually re-associate all of the fields, but that is what I'm trying to avoid just to save time.
Ok figured it out!! Manage Database, double click the table that is in the Relationships tab, and select the different table there. Bingo!