This is what I came up with (before seeing Josh W. answer, well actually I saw it but skimmed it so fast I misunderstood it):
declare @name nvarchar(100)
select @name = [name] from sys.objects where type = 'D' and parent_object_id = object_id('sometable')
if (@name is not null)
begin
exec ('alter table sometable drop constraint ' + @name)
end
The advantage I have here is that I know that there is only one such constraint on the whole table. If there had been two, well I guess that is why you are supposed to name them ;).
(The issues is that that this is a modification made to 10 different customer databases, so there isn't one consistent name to put in a script)