How to programatically change the login audit settings?
Sure, here are the commands listed below. (Reformatted from original post for reading ease.)

These can derived from clicking on Server Properties, then choosing the Security tab and changing the Login auditing settings and scripting out the code, instead of clicking on the OK button to close the dialog.  This type of scripting is usually an option on actions taken through the SSMS interface.  

USE [master]
GO
EXEC xp_instance_regwrite N'HKEY_LOCAL_MACHINE', 
   N'Software\Microsoft\MSSQLServer\MSSQLServer', 
   N'AuditLevel', REG_DWORD, 0 -- None
GO
EXEC xp_instance_regwrite N'HKEY_LOCAL_MACHINE', 
   N'Software\Microsoft\MSSQLServer\MSSQLServer', 
   N'AuditLevel', REG_DWORD, 1 -- Successful Only
GO
EXEC xp_instance_regwrite N'HKEY_LOCAL_MACHINE', 
   N'Software\Microsoft\MSSQLServer\MSSQLServer', 
   N'AuditLevel', REG_DWORD, 2 -- Failed only
GO
EXEC xp_instance_regwrite N'HKEY_LOCAL_MACHINE', 
   N'Software\Microsoft\MSSQLServer\MSSQLServer', 
   N'AuditLevel', REG_DWORD, 3 -- Failed &amp; Successful
GO


So, for your requirement just set the key to 0 (no auditing) then back to 2 (failed only).

But, alas, as Shawn Melton pointed out, it requires the server to be restarted before the change can be applied. Of course, you can program for restarting the server as well. Does allowing a restart (or 2 restarts) fit into your process?