Here is a script that will delete the column along with its default constraint. Replace MYTABLENAME and MYCOLUMNNAME appropriately.
declare @constraint_name sysname, @sql nvarchar(max)
select @constraint_name = name
from sys.default_constraints
where parent_object_id = object_id('MYTABLENAME')
AND type="D"
AND parent_column_id = (
select column_id
from sys.columns
where object_id = object_id('MYTABLENAME')
and name="MYCOLUMNNAME"
)
set @sql = N'alter table MYTABLENAME drop constraint ' + @constraint_name
exec sp_executesql @sql
alter table MYTABLENAME drop column MYCOLUMNNAME
go