Drop un-named constraint

declare @name nvarchar(32),
@sql nvarchar(1000)

-- find constraint name
select @name = O.name
from sysobjects AS O
left join sysobjects AS T
on O.parent_obj = T.id
where isnull(objectproperty(O.id,'IsMSShipped'),1) = 0
and O.name not like '%dtproper%'
and O.name not like 'dt[_]%'
and T.name = 'MyTable'
and O.name like 'My Column%'

-- delete if found
if not @name is null
begin
select @sql = 'ALTER TABLE [MyTable] DROP CONSTRAINT [' + @name + ']'
execute sp_executesql @sql
end

-- do your ALTER TABLE here

-- replace the constraint
select @sql = 'ALTER TABLE [MyTable] ADD CONSTRAINT [' + @name + '] DEFAULT (0) FOR [MyColumn]'
execute sp_executesql @sql