Using sys.dm_os_performance_counters and DIFF to display logins per second
Sorry, think this should work.

DECLARE @CurrentLoginUser int
DECLARE @CurrentLoginUser1 int


SET @CurrentLoginUser = (SELECT cntr_value AS [LoginsPerSec] FROM sys.dm_os_performance_counters WHERE object_name = 'SQLServer:General Statistics' AND counter_name = 'Logins/sec')
WAITFOR DELAY '000:00:01'
SET @CurrentLoginUser1 = (SELECT cntr_value AS [LoginsPerSec] FROM sys.dm_os_performance_counters WHERE object_name = 'SQLServer:General Statistics' AND counter_name = 'Logins/sec')

SELECT @CurrentLoginUser1 - @CurrentLoginUser