You just set a default value in the new columns and that will allow you to add them.
alter table table_name
add column_name datetime not null
constraint DF_Default_Object_Name default (getdate())
or this one for a varchar field.
alter table table_name
add column_name varchar(10) not null
constraint DF_Default_Object_Name default ('A')
You can also drop the default if you do not need it after you added the column.
alter table table_name
drop constraint DF_Default_Object_Name