Add a column to a table, if it does not already exist

You can use a similar construct by using the sys.columns table io sys.objects.

IF NOT EXISTS (
  SELECT * 
  FROM   sys.columns 
  WHERE  object_id = OBJECT_ID(N'[dbo].[Person]') 
         AND name = 'ColumnName'
)

IF COL_LENGTH('table_name', 'column_name') IS NULL
BEGIN
    ALTER TABLE table_name
    ADD [column_name] INT
END

Another alternative. I prefer this approach because it is less writing but the two accomplish the same thing.

IF COLUMNPROPERTY(OBJECT_ID('dbo.Person'), 'ColumnName', 'ColumnId') IS NULL
BEGIN
    ALTER TABLE Person 
    ADD ColumnName VARCHAR(MAX) NOT NULL
END

I also noticed yours is looking for where table does exist that is obviously just this

 if COLUMNPROPERTY( OBJECT_ID('dbo.Person'),'ColumnName','ColumnId') is not null

Here's another variation that worked for me.

IF NOT EXISTS (SELECT 1
        FROM INFORMATION_SCHEMA.COLUMNS
        WHERE upper(TABLE_NAME) = 'TABLENAME'
        AND upper(COLUMN_NAME) = 'COLUMNNAME')
BEGIN
    ALTER TABLE [dbo].[Person] ADD Column
END
GO

EDIT: Note that INFORMATION_SCHEMA views may not always be updated, use SYS.COLUMNS instead:

IF NOT EXISTS (SELECT 1 FROM SYS.COLUMNS....

IF NOT EXISTS (SELECT * FROM syscolumns
  WHERE ID=OBJECT_ID('[db].[Employee]') AND NAME='EmpName')
  ALTER TABLE [db].[Employee]
  ADD [EmpName] VARCHAR(10)
GO

I Hope this would help. More info