You can easily implement your requirement using a trigger on Login table that will log info in the audit_login table.
the key is using table trigger to log info in the audit table for auditing.
I will see if I can provide a working code. But you got the idea now.
Update: below is a prototype code that will help you.
Note: you dont need any Stored procedure, A trigger will do the job.
You can put try/catch to handle errors, which I have not done as this is only to help you understand the concept.
IF EXISTS (SELECT * FROM sys.objects WHERE object_id = OBJECT_ID(N'[dbo].[Logins]') AND type in (N'U'))
DROP TABLE [dbo].[Logins]
GO
create table Logins (userid varchar(15) not null
,username varchar(max)
,[password] varchar(50)
,[status] varchar(1)) -- S = Success, F= Fail
go
IF EXISTS (SELECT * FROM sys.objects WHERE object_id = OBJECT_ID(N'[dbo].[audit_login]') AND type in (N'U'))
DROP TABLE [dbo].[audit_login]
GO
SELECT [userid],[username],[status]
,AuditDataState=CONVERT(VARCHAR(10),'')
,AuditDMLAction=CONVERT(VARCHAR(10),'')
,AuditUser =CONVERT(SYSNAME,'')
,AuditDateTime=CONVERT(DATETIME,'01-JAN-1900')
into dbo.audit_login
FROM dbo.Logins
WHERE 1=2
go
CREATE TRIGGER Logins_Insert
ON dbo.Logins
FOR INSERT
AS
INSERT INTO dbo.audit_login
SELECT [userid],[username],[status],'New','Insert',SUSER_SNAME(),getdate() FROM INSERTED
GO
CREATE TRIGGER Logins_Delete
ON dbo.Logins
FOR DELETE
AS
INSERT INTO dbo.audit_login
SELECT [userid],[username],[status],'Old','Delete',SUSER_SNAME(),getdate() FROM DELETED
GO
CREATE TRIGGER Logins_Update
ON dbo.Logins
FOR UPDATE
AS
INSERT INTO dbo.audit_login
SELECT [userid],[username],[status],'New','Update',SUSER_SNAME(),getdate() FROM INSERTED
INSERT INTO dbo.audit_login
SELECT [userid],[username],[status],'Old','Update',SUSER_SNAME(),getdate() FROM DELETED
GO
Now insert some data :
-- Insert New Data
insert into Logins
values ('kin001', 'kin','$tr0ng01','s')
select * from audit_login
-- Update the current Data
update Logins
set userid = 'kin-up-01'
where userid = 'kin001'
select * from audit_login
-- delete the data
delete from Logins
where userid = 'kin-up-01'
Below will be the end result: