How to drop SQL default constraint without knowing its name?

Expanding on Mitch Wheat's code, the following script will generate the command to drop the constraint and dynamically execute it.

declare @schema_name nvarchar(256)
declare @table_name nvarchar(256)
declare @col_name nvarchar(256)
declare @Command  nvarchar(1000)

set @schema_name = N'MySchema'
set @table_name = N'Department'
set @col_name = N'ModifiedDate'

select @Command = 'ALTER TABLE ' + @schema_name + '.[' + @table_name + '] DROP CONSTRAINT ' + d.name
 from sys.tables t
  join sys.default_constraints d on d.parent_object_id = t.object_id
  join sys.columns c on c.object_id = t.object_id and c.column_id = d.parent_column_id
 where t.name = @table_name
  and t.schema_id = schema_id(@schema_name)
  and c.name = @col_name

--print @Command

execute (@Command)

Rob Farley's blog post might be of help:

• Two ways to find / drop a default constraint without knowing its name

Something like:

 declare @table_name nvarchar(256)
 declare @col_name nvarchar(256)
 set @table_name = N'Department'
 set @col_name = N'ModifiedDate'

 select t.name, c.name, d.name, d.definition
 from 
     sys.tables t
     join sys.default_constraints d on d.parent_object_id = t.object_id
     join sys.columns c on c.object_id = t.object_id
                           and c.column_id = d.parent_column_id
 where 
     t.name = @table_name
     and c.name = @col_name